Solve the absolute value equation or indicate that the equation has no solution.
-$\left| x ^ { 2 } - 4 x - 4 \right| = 8$
A) $\{ - 2,2,6 \}$
B) $\{ - 2,2 \}$
C) $\{ - 2,2 , - 6 \}$
D) $\{ 2,6 \}$

Question

Quizplus · Accepted Answer

To solve the absolute value equation $\left| x ^ { 2 } - 4 x - 4 \right| = 8$, we consider two cases: when the expression inside the absolute value is positive or zero, and when it is negative.1. $x^2 - 4x - 4 = 8$Solving this quadratic equation:$x^2 - 4x - 12 = 0$Factoring or using the quadratic formula, we find:$x = 2 + \sqrt{16} = 6$ or $x = 2 - \sqrt{16} = -2$2. $x^2 - 4x - 4 = -8$Solving this quadratic equation:$x^2 - 4x + 4 = 0$Factoring or using the quadratic formula, we find:$x = 2 + \sqrt{0} = 2$ or $x = 2 - \sqrt{0} = 2$Thus, the solution set is $\{ - 2,2,6 \}$.

Solve the Absolute Value Equation or Indicate That the Equation ∣x2−4x−4∣=8\left| x ^ { 2 } - 4 x - 4 \right| = 8​x2−4x−4​=8

Solve the Absolute Value Equation or Indicate That the Equation $\left| x ^ { 2 } - 4 x - 4 \right| = 8$