What is the solution to the equation x2 + 6x=40

x=10 x=-4

Step-by-step explanation:

x^2 + 6x = 40

subtract 40 from each side

x^2 + 6x - 40 = 0

what numbers multiply to - 40 and add to 6

-10 * 4 = - 40 - 10 + 4 = 6

(x-10) (x+4) = 0

using the zero product property

x-10 = 0 x+4 = 0

x=10 x=-4

x² + 6x = 40 Subtract 40 on both sides to get the equation equal to 0.

x² + 6x - 40 = 0

Now you need to factor the equation. To do so, you find the factors of 40 that add or subtract to 6.

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

[1 * 40, 2 * 20, 4 * 10, 5 * 8]

4 and 10 subtracts to 6.

Instead of 6x:

x² + 6x - 40 = 0

You can replace 6x with:

x² - 4x + 10x - 40 = 0 [this is because the sum of - 4x and 10x is 6x]

Now factor the equation separately. Factor out x in (x² - 4x), and factor out 10 in (10x - 40)

x (x - 4) + 10 (x - 4) = 0 Factor out (x - 4)

(x - 4) (x + 10) = 0

x - 4 = 0 Add 4 on both sides

x = 4

x + 10 = 0 Subtract 10 on both sides

x = - 10

x = 4, x = - 10