Question

Solve the quadratic equation by completing the square.

Answer 1

Answer:

x = - 1, x = 8

Step-by-step explanation:

Given

x² - 7x - 8 = 0 ( add 8 to both sides )

x² - 7x = 8

To complete the square

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

x² + 2(- $\frac{7}{2}$ )x + $\frac{49}{4}$ = 8 + $\frac{49}{4}$ = $\frac{81}{4}$

(x - $\frac{7}{2}$ )² = $\frac{81}{4}$ ( take the square root of both sides )

x - $\frac{7}{2}$ = ± $\sqrt{\frac{81}{4} }$ = ± $\frac{9}{2}$ ( add $\frac{7}{2}$ to both sides )

x = $\frac{7}{2}$ ± $\frac{9}{2}$

Thus

x = $\frac{7}{2}$ - $\frac{9}{2}$ =  $\frac{-2}{2}$ = - 1

x = $\frac{7}{2}$ + $\frac{9}{2}$ = $\frac{16}{2}$ = 8

Answer 2

Answer:

x'1 = -1

x'2 = 8

Step-by-step explanation: