Question

X²- 6x = 7 FInd the soultion to the equation by completing the square

Answer 1

x=-1 , x=7

Explanation:

x²-6x-7=0

(x)² - 2(x)(3) +(3)² -7 - (3)²=0------------(adding and removing 9 to make it a complete square)

(x-3)² -7-9=0

(x-3)²-16=0

(x-3)² - (4)²= 0

(x-3+4)(x-3-4)=0

(x+1)(x-7)=0

(x+1)=0⇒x=-1

(x-7)=0⇒x=7

Answer 2

x = - 1, x = 7

Explanation:

Given

x² - 6x = 7

To complete the square

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

x² + 2(- 3) x + 9 = 7 + 9

(x - 3)² = 16 ( take the square root of both sides )

x - 3 = ±
`√(16)` = ± 4

Add 3 to both sides

x = 3 ± 4, that is

x = 3 + 4 = 7 or x = 3 - 4 = - 1