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mr-mathematics.com Recapping: Algebraic notation and square numbers.
x and y are both integers and greater than zero. Find the values of x and y. ANS mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0 b) x2 + 2x - 4 = 0 c) x2 + 8x + 5 = 0 d) x2 – 2x – 3 = 0 e) x2 - x - 2 = 0 f) x2 – 5x – 4 = 0 ANS ANS ANS ANS ANS ANS mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 g) x2 + 3 = 5x h) x2 = 5 - 9x ANS ANS ANS ANS ANS ANS ANS ANS mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. The area of the shape is 20 cm². ANS a) Set up an equation in terms of x. b) Solve the equation to find the value of x. Leave your answer in simplified surd form. mr-mathematics.com
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mr-mathematics.com Recapping: Algebraic notation and square numbers.
x and y are both integers and greater than zero. Find the values of x and y. x = 7, y = 2 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0 c) x2 + 8x + 5 = 0 d) x2 – 2x – 3 = 0 e) x2 - x - 2 = 0 f) x2 – 5x – 4 = 0 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0, 𝑥=−1±√5 c) x2 + 8x + 5 = 0 d) x2 – 2x – 3 = 0 e) x2 - x - 2 = 0 f) x2 – 5x – 4 = 0 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0, 𝑥=−1±√5 c) x2 + 8x + 5 = 0, 𝑥=−4±√11 d) x2 – 2x – 3 = 0 e) x2 - x - 2 = 0 f) x2 – 5x – 4 = 0 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0, 𝑥=−1±√5 c) x2 + 8x + 5 = 0, 𝑥=−4±√11 d) x2 – 2x – 3 = 0, x = -1, x = 3 e) x2 - x - 2 = 0 f) x2 – 5x – 4 = 0 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0, 𝑥=−1±√5 c) x2 + 8x + 5 = 0, 𝑥=−4±√11 d) x2 – 2x – 3 = 0, x = -1, x = 3 e) x2 - x - 2 = 0, x = -1, x = 2 f) x2 – 5x – 4 = 0 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x + 8 = 0, x = -4, x = -2 b) x2 + 2x - 4 = 0, 𝑥=−1±√5 c) x2 + 8x + 5 = 0, 𝑥=−4±√11 d) x2 – 2x – 3 = 0, x = -1, x = 3 e) x2 - x - 2 = 0, x = -1, x = 2 f) x2 – 5x – 4 = 0, 𝑥= 5 ± √41 2 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 𝑥=6±√34 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 𝑥=6±√34 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 𝑥=3±2√2 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 𝑥=6±√34 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 𝑥=3±2√2 𝑥=−1±√3 g) x2 + 3 = 5x h) x2 = 5 - 9x Go Back mr-mathematics.com
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𝑥= 5 ± √13 2 mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 𝑥=6±√34 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 𝑥=3±2√2 𝑥=−1±√3 g) x2 + 3 = 5x h) x2 = 5 - 9x 𝑥= 5 ± √13 2 Go Back mr-mathematics.com
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𝑥= 5 ± √13 2 𝑥= −9 ± √101 2 mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. Solve these equations by completing the square: a) x2 + 6x – 4 = 0 b) x2 + 8x + 3 = 0 𝑥=−3±√13 𝑥=−4±√13 c) x2 – 10x + 6 = 0 d) x2 – 12x + 2 = 0 𝑥=5±√19 𝑥=6±√34 e) x2 – 6x + 1 = 0 f) x2 + 2x = 2 𝑥=3±2√2 𝑥=−1±√3 g) x2 + 3 = 5x h) x2 = 5 - 9x 𝑥= 5 ± √ 𝑥= −9 ± √101 2 Go Back mr-mathematics.com
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mr-mathematics.com Completing the Square
Learning Objective: Solve a quadratic equation by completing the square. The area of the shape is 20 cm². a) Set up an equation in terms of x. x2 + 5x – 18 = 0 b) Solve the equation to find the value of x. Leave your answer in simplified surd form. 𝑥= −5±√97 2 Go Back mr-mathematics.com
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