Question

How do you complete the square for the quadratic expression x ² −6x−7?

A) x ² −6x+9−16
B) x ² −6x+9−2
C) x ² −6x+9−16+7
D) x ² −6x+9+16

Answer 1

To complete the square for the quadratic expression x² − 6x − 7, follow these steps: 1) Move the constant term to the right side. 2) Take half of the coefficient of x and square it. 3) Add the squared value to both sides. 4) Re-write the equation as a perfect square trinomial. 5) Simplify the equation.

Step-by-step explanation:

To complete the square for the quadratic expression x² − 6x − 7, we follow these steps:

1. Move the constant term (-7) to the right side of the equation.
2. Take half of the coefficient of x (-6/2 = -3) and square it to get 9.
3. Add 9 to both sides of the equation.
4. Re-write the equation as a perfect square trinomial (x² - 6x + 9).
5. Finally, simplify the equation by combining like terms.

Therefore, the completed square form of x² − 6x − 7 is x² - 6x + 9 - 16. The correct answer is option A) x² - 6x + 9 - 16.