1. Adapted from Walch Education
Completing the Square
Adapted from Walch Education

2. Perfect Square Trinomial
can be written as the square of a binomial is called a perfect square trinomial
When the binomial (x + a) is squared, the resulting perfect square trinomial is x2 + 2ax + a2.
When the binomial (ax + b) is squared, the resulting perfect square trinomial is a2x2 + 2abx + b2.
5.2.3: Completing the Square

3. 5.2.3: Completing the Square
Completing the Square to Solve Quadratics
Make sure the equation is in standard form, ax2 + bx + c.
Subtract c from both sides.
Divide each term by a to get a leading coefficient of 1.
Add the square of half of the coefficient of the x-term to both sides to complete the square.
Express the perfect square trinomial as the square of a binomial.
Solve by using square roots.
5.2.3: Completing the Square

4. 5.2.3: Completing the Square
Practice
Solve x2 + 6x + 4 = 0 by completing the square.
5.2.3: Completing the Square

5. 5.2.3: Completing the Square
Complete the Square
x2 + 6x + 4 = 0
Original equation
x2 + 6x = –4
Subtract 4 from both sides.
x2 + 6x + 32 = –4 + 32
Add the square of half of the coefficient of the x-term to both sides to complete the square.
x2 + 6x + 9 = 5
Simplify.
5.2.3: Completing the Square

6. Express the perfect square trinomial as the square of a binomial
Half of b is 3, so the left side of the equation can be written as (x + 3)2. (x + 3)2 = 5
5.2.3: Completing the Square

7. 5.2.3: Completing the Square
Isolate x
(x + 3)2 = 5
Equation
Take the square root of both sides.
Subtract 3 from both sides.
The equation x2 + 6x + 4 = 0 has two solutions,
5.2.3: Completing the Square

8. 5.2.3: Completing the Square
Try this one.
Solve 5x2 – 50x – 120 = 0 by completing the square.
5.2.3: Completing the Square

9. Ms. Dambreville
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