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Chapter 0: Problem 65

Solve each quadratic equation by the square root property. $$3(x-4)^{2}=15$$

Short Answer

Expert verified
The solutions to the equation are \(x = 4 + \sqrt{5}\) and \(x = 4 - \sqrt{5}\).

Step by step solution

01

Simplify the Equation

Divide each side of the equation \(3(x-4)^{2}=15\) by 3 to isolate the squared term. This gives us \((x-4)^{2}=5\).
02

Apply the Square Root Property

Take the square root of each side of the equation \((x-4)^{2}=5\). According to the Square Root Property, this yields two equations: \(x-4 = \sqrt{5}\) and \(x-4 = -\sqrt{5}\).
03

Solve for x

Solving both equations for x gives us \(x = 4 + \sqrt{5}\) and \(x = 4 - \sqrt{5}\).

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