Question

Consider this question:

-2x=x^2-6

1) Rewrite the question by completing the square. Your equation should look like (x+c)^2=d or (x-c)^2=d.

2) What are the solutions to the equation?

Answer 1

Answer:

see explanation

Step-by-step explanation:

(1)

Given

- 2x = x² - 6 ( subtract x² from both sides )

- x² - 2x = - 6 ( multiply through by - 1 )

x² + 2x = 6

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(1)x + 1 = 6 + 1

(x + 1)² = 7

(2)

Take the square root of both sides

x + 1 = ± $\sqrt{7}$ ( subtract 1 from both sides )

x = - 1 ± $\sqrt{7}$

Solutions are x = - 1 - $\sqrt{7}$ , x = - 1 + $\sqrt{7}$