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Chapter 0: Problem 129

Solve each equation. $$\left|x^{2}+2 x-36\right|=12$$

Short Answer

Expert verified
The solutions to the absolute value equation are x = 4 and x = -6.

Step by step solution

01

Solve \(x^{2}+2 x-36 = 12\)

First, subtract 12 from both sides, simplifying to \(x^{2}+2 x-24 = 0\). This is now a quadratic equation which can be factored to \((x - 4)(x + 6) = 0\). Set each factor equal to zero and solve for x to get the solutions x = 4, x = -6.
02

Solve \(x^{2} +2 x -36 = -12\)

Again, we subtract -12 from both sides, getting \(x^{2}+2 x-24 = 0\). This quadratic equation has the same factors as the previous one, \((x - 4)(x + 6) = 0\), and so the solutions are again x = 4, x = -6.
03

Consolidate the Solution Set

Now, combine the solution sets from the two equations to find a single, consolidated set of solutions. In this case, both equations returned the same solutions, so the consolidated solution set is simply x = 4, x = -6.

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