Question

Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.

x = –7 or x = 6
x = –7 or x = –6
x = –6 or x = 7
x = 6 or x = 7

Answer 1

x^2 + x - 30 = 12

x^2 + x - 42 = 0
(x+7)(x-6) = 0
if the product of two numbers is zero, then at least one of them must be zero.
So, either
x+7 = 0
or
x-6 = 0

Answer 2

jb./kn

Answer 3

[AI-generated answer — Explain Bot]

To use the zero product property to find the solutions to the equation x^2 + x - 30 = 12, you need to set the equation equal to zero first.

Start by moving the constant term (-12) to the other side of the equation, so that you have:
x^2 + x - 30 - 12 = 0
Simplify the equation by combining like terms:
x^2 + x - 42 = 0

Now, you can factor the quadratic equation to solve for x.

The factors of -42 that add up to 1 (which is the coefficient of the x term) are -6 and 7, since -6 + 7 = 1.

So, the factored form of the equation is:
(x - 6)(x + 7) = 0

Next, set each factor equal to zero and solve for x:
x - 6 = 0 or x + 7 = 0

For the first equation, add 6 to both sides:
x = 6

For the second equation, subtract 7 from both sides:
x = -7

Therefore, the solutions to the equation x^2 + x - 30 = 12 are x = 6 or x = -7.