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Chapter 1: Problem 26

If \(\frac{(4 x+3)^2}{2}=72\) and \(x>0\), then \(x=\)

Short Answer

Expert verified
So, when \(x > 0\), the value of \(x = \frac{9}{4}\).

Step by step solution

01

Multiply by 2

To eliminate the fraction, multiply both sides of the equation by 2: \[(4x+3)^2=144\]
02

Take the square root

Now, take the square root of both sides of the equation to get rid of the square: \[4x+3=\pm\sqrt{144}\] Since \(x>0\), we have: \[4x+3=12\]
03

Isolate x

Subtract 3 from both sides of the equation to isolate \(x\): \[4x=9\]
04

Solve for x

Finally, divide both sides of the equation by 4 to solve for \(x\): \[x=\frac{9}{4}\]

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