Question

solve the equation using square roots. select the solution(s)
$(2x - 1)^2 = 81$

Explanation:

Step 1: Take square root of both sides

Given the equation \((2x - 1)^2 = 81\), we take the square root of both sides. Remember that \(\sqrt{a^2}=\pm a\), so we have:
\[
2x - 1=\pm\sqrt{81}
\]
Since \(\sqrt{81} = 9\), this simplifies to:
\[
2x - 1=\pm9
\]

Step 2: Solve for \(x\) in two cases

Case 1: \(2x - 1 = 9\)

Add 1 to both sides:
\[
2x=9 + 1
\]
\[
2x=10
\]
Divide both sides by 2:
\[
x=\frac{10}{2}=5
\]

Case 2: \(2x - 1=-9\)

Add 1 to both sides:
\[
2x=-9 + 1
\]
\[
2x=-8
\]
Divide both sides by 2:
\[
x=\frac{-8}{2}=-4
\]

Answer:

The solutions are \(x = 5\) and \(x=-4\)