Completing the Square.

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Solving Quadratic Equations by Completing the Square

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Presentation transcript:

Completing the Square

Warm-Up x2 + 20x + ___ x2 - 4x + ___ x2 + 10x + ___ x2 + 22x + ___ Create Perfect Square Trinomials. Write the SQUARES of BINOMIALS ==== x2 + 20x + ___ x2 - 4x + ___ x2 + 10x + ___ x2 + 22x + ___ x2 - 8x + ___ x2 + 12x + ___ 2

Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation +20 +20

Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

Examples: 2. x2 +2x-8=0 3. x2 +6x-5=0 4. x2 -12x+4=0

Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers. 1. x2 +2x-63=0 2. x2 +8x-84=0 3. x2 -6x-4=0 4. x2 -10x+2=0

PRACTICE A. x2 -12x+____, (____)2 B. x2 +7x +____, (____)2 1.Complete the PST and write the squares of binomial: A. x2 -12x+____, (____)2 B. x2 +7x +____, (____)2 A. x2 -8x+12=0, x=___ x=___ B. x2 +10x-2=0, x=___ x=___ 36 x - 6 49/4 X+7/2 II. Solve for X by COMPLETING THE SQUARE: 6 2 -5+√27 -5-√27