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

Solution:

Zero product property, also known as zero product principle states that if p × q = 0 , then p = 0 or q = 0 or both p = 0 and q = 0 .

Given: Quadratic equation is x² + x - 30 = 12

It can be written as

x² + x - 30 - 12 = 0

x²  + x - 42 = 0

By splitting the middle term

x² + 7x - 6x - 42 = 0

Taking out the common terms

x(x + 7) - 6(x + 7) = 0

So we get,

(x + 7)(x - 6) = 0

Now according to the zero product property,

either x + 7 = 0 or x - 6 = 0

x = -7 or x = 6

Therefore, the solution is -7 or 6.

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

Summary:

Using the zero product property, the solutions to the equation x² + x - 30 = 12 is -7 or 6.