Question

Solve by factoring or finding square roots x^2-6x-7=0

Answer 1

x = - 1, x = 7

Explanation:

Given

x² - 6x - 7 = 0

Consider the factors of the constant term (- 7 ) which sum to give the coefficient of the x- term

The factors are - 7 and + 1, since

- 7 × 1 = - 7 and - 7 + 1 = - 6, hence

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

Equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x + 1 = 0 ⇒ x = - 1

Answer 2

x = -1 or x = 7

Explanation:

`x^2-6x-7=0\\\\x^2+x-7x-7=0\\\\x(x+1)-7(x+1)=0\\\\(x+1)(x-7)=0\iff x+1=0\ \vee\ x-7=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\bold{x=-1}\\\\x-7=0\qquad\text{add 7 to both sides}\\\bold{x=7}`