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−1(2x−8)2=−144-1(2x-8)^2=-144

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Full solution

Q. −1(2x−8)2=−144-1(2x-8)^2=-144
  1. Take Square Root: Now, take the square root of both sides to solve for 2x−82x-8.(2x−8)2=±144\sqrt{(2x-8)^2} = \pm\sqrt{144}2x−8=±122x - 8 = \pm12
  2. Solve for x (Positive Root): Next, we'll solve for x by adding 88 to both sides of the equation.\newlineFor the positive root:\newline2x−8+8=12+82x - 8 + 8 = 12 + 8\newline2x=202x = 20
  3. Isolate x (Positive Root): Divide both sides by 22 to isolate xx.2x2=202\frac{2x}{2} = \frac{20}{2}x=10x = 10
  4. Solve for x (Negative Root): Now, let's solve for the negative root.\newline2x−8+8=−12+82x - 8 + 8 = -12 + 8\newline2x=−42x = -4
  5. Isolate x (Negative Root): Divide both sides by 22 to isolate x.\newline2x2=−42\frac{2x}{2} = \frac{-4}{2}\newlinex=−2x = -2

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