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\( x = \frac{1}{16} \) or \( x = 0.0625 \)
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To solve the equation \( 4 \sqrt{x+3} - 5 = 2 \), first add 5 to both sides: \[ 4 \sqrt{x+3} = 2 + 5 \] This simplifies to: \[ 4 \sqrt{x+3} = 7 \] Next, divide both sides by 4: \[ \sqrt{x+3} = \frac{7}{4} \] Now, to eliminate the square root, square both sides: \[ x + 3 = \left(\frac{7}{4}\right)^2 \] Calculating the right side gives: \[ x + 3 = \frac{49}{16} \] To isolate \(x\), subtract 3 (or \(\frac{48}{16}\)) from both sides: \[ x = \frac{49}{16} - \frac{48}{16} \] Thus, we have: \[ x = \frac{1}{16} \] So the solution is: \[ \boxed{\frac{1}{16}} \]
