Question

given ((x - 7)^2 = 36), select the values of (x).
□ (x = 13)
□ (x = 1)
□ (x = -29)
□ (x = 42)
done

Explanation:

Step1: Take square root of both sides

To solve \((x - 7)^2 = 36\), we take the square root of both sides. Remember that if \(y^2 = a\) (where \(a\geq0\)), then \(y=\pm\sqrt{a}\). So applying this to our equation, we get:
\(x - 7=\pm\sqrt{36}\)
Since \(\sqrt{36} = 6\), this simplifies to:
\(x - 7=\pm6\)

Step2: Solve for x in two cases

Case 1: When we take the positive sign (\(x - 7 = 6\))

Add 7 to both sides of the equation:
\(x=6 + 7\)
\(x = 13\)

Case 2: When we take the negative sign (\(x - 7=-6\))

Add 7 to both sides of the equation:
\(x=-6 + 7\)
\(x = 1\)

Answer:

\(x = 13\) and \(x = 1\) (corresponding to the options: \(x = 13\), \(x = 1\))