In Exercises 101–106, solve each equation. ∣x2+2x−36∣=12|$$x^2 + 2x - 36$$| = 12

Ch. 1 - Equations and Inequalities

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Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problema 103

Capitolo 2, Problema 103

In Exercises 101–106, solve each equation. $∣ x^{2} + 2 x - 36 ∣ = 12$

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Recognize that the equation involves an absolute value: $|x^2 + 2x - 36| = 12$. This means the expression inside the absolute value can be either 12 or -12.

Set up two separate equations to remove the absolute value: 1) $x^2 + 2x - 36 = 12$ 2) $x^2 + 2x - 36 = -12$

Solve the first quadratic equation: $x^2 + 2x - 36 = 12$. Start by moving all terms to one side to set the equation to zero: $x^2 + 2x - 36 - 12 = 0$, which simplifies to $x^2 + 2x - 48 = 0$.

Solve the second quadratic equation: $x^2 + 2x - 36 = -12$. Move all terms to one side: $x^2 + 2x - 36 + 12 = 0$, which simplifies to $x^2 + 2x - 24 = 0$.

For each quadratic equation, use factoring, completing the square, or the quadratic formula to find the values of $x$ that satisfy the equation.

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