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Chapter 0: Problem 66

Solve each quadratic equation by the square root property. $$3(x+4)^{2}=21$$

Short Answer

Expert verified
The solution to the quadratic equation \(3(x+4)^2 = 21\) is \(x = -4 \pm \sqrt{7}\).

Step by step solution

01

Simplify the equation

Divide each side of the equation \(3(x+4)^2 = 21\) by 3 to simplify. The equation then becomes \((x+4)^2 = 7\).
02

Apply the square root

Taking the square root of both sides results in \(x+4 = \pm \sqrt{7}\). Here, note that - when we take the square root of both sides, it's necessary to include both the positive and negative square roots.
03

Isolate 'x'

To isolate 'x', subtract 4 from both sides of the equation resulting in \(x = -4 \pm \sqrt{7}\). That is the final solution and is in the correct form.

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