Question

What are the solutions to X2 + 8X + 7 = 0?

Answer 1

`x=-1,-7`

Explanation:

`x^2+8x+7=0` where a
`\\eq` 0 so a = 1 b = 8 c = 7

Quadratic Formula:
`x=-b(√(b^2-4ac) )/(2a)`

`x=-8(√(8^2-4(1)(7)) )/(2(1))`

`x=-8(√(64-28) )/(2)` Evaluate the exponent and multiply 4ac

`x=-8(√(36) )/(2)` Subtract b^2 - 4ac and multiply 2a

`x=-8(√(6) )/(2)` Solve for the sqrt root of 35

x = - 8 ± 6/2 =

x = - 8 + 6/2 = -1

x = - 8 - 6/2 = -7

Answer 2

x = - 7, x = - 1

Explanation:

Given

x² + 8x + 7 = 0

Consider the factors of the constant term (+ 7) which sum to give the coefficient of the x- term (+ 8)

The factors are + 7 and + 1 , since

7 × 1 = 7 and 7 + 1 = 8 , then

(x + 7)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 1 = 0 ⇒ x = - 1