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