Question

What are the solutions to the equation?

x2 + 6x=40

x=-10 and x = 4

0 x=-5 and x = 8
0 x =-4 and x = 10

Answer 1

So firstly, you want to set your equation to zero. You can do this by subtracting 40 on both sides of the equation. $x^2+6x-40=0$

Now, what two numbers add up to 6x and multiply to -40x^2? 10x and -4x. With this info, replace 6x with 10x and -4x: $x^2-4x+10x-40=0$

Next, factor x^2-4x and 10x-40 separately. Make sure that what's inside the parentheses is the same: $x(x-4)+10(x-4)=0$

Now you can rewrite the equation as: $(x+10)(x-4)=0$

Now using Zero Product Property, solve for x:

$x+10=0\\ x=-10$

$x-4=0\\ x=4$

In short, x = -10 and 4.