Question

An equation is shown.

x² + 7x 21 = 9
What are the two solutions to the equation?
X =
X =
1
st
4
2
5
3
6

Answer 1

x = - 10 , x = 3

Explanation:

x² + 7x - 21 = 9 ( subtract 9 from both sides )

x² + 7x - 30 = 0 ← in standard form

consider the factors of the constant term (- 30) which sum to give the coefficient of the x- term (+ 7)

the factors are + 10 and - 3 , since

+ 10 × - 3 = - 30 and = 10 - 3 = + 7 , then

x² + 7x - 30 = 0

(x + 10)(x - 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 10 = 0 ( subtract 10 from both sides )

x = - 10

x - 3 = 0 ( add 3 to both sides )

x = 3

solutions are x = - 10 , x = 3