Solve the quadratic equation by completing the square.

Question

asked Feb 24, 2021 191k views

2 Answers

Nazra · Answer 1 · 2021-02-26T22:20:11+0000

Answer:

x = - 1, x = 8

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(-
(7)/(2) )x +
(49)/(4) = 8 +
=
(81)/(4)

(x -
(7)/(2) )² =
(81)/(4) ( take the square root of both sides )

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

x =
(7)/(2) ±
(9)/(2)

Thus

x =
(7)/(2) -
(9)/(2) =
(-2)/(2) = - 1

x =
(7)/(2) +
(9)/(2) =
(16)/(2) = 8