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Chapter 0: Problem 64

Solve each quadratic equation by the square root property. $$3 x^{2}-1=47$$

Short Answer

Expert verified
The solutions to the quadratic equation \(3 x^{2}-1=47\) are x = 4 and x = -4.

Step by step solution

01

Rearrange Equation

Rearrange the equation \(3x^{2}-1=47\) to isolate the \(x^{2}\) term. This is done by adding 1 to both sides to get rid of the -1 on the left side and then dividing by 3 to isolate \(x^{2}\). This gives the equation: \(3x^{2} = 48\), which simplifies to \(x^{2} = 16\) when divided by 3.
02

Apply the Square Root Property

Now that \(x^{2} = 16\), apply the square-root property which states that if \(x^{2} = a\), then \(x = 卤 \sqrt{a}\). So we have \(x = 卤 \sqrt{16}\).
03

Evaluate the Square Root

\(\sqrt{16}\) is 4, so we have \(x = 卤 4\). This means the equation \(3x^{2}-1=47\) has two solutions, x = 4 and x = -4.

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