Question

solve ((x - 3)^2 = 49). select the values of (x). (square) (-46) (square) (-4) (square) (10) (square) (52)

Explanation:

Step1: Take square root of both sides

To solve the equation \((x - 3)^2 = 49\), we take the square root of both sides. Remember that when we take the square root of a number, we get both a positive and a negative solution. So we have:
\[
\sqrt{(x - 3)^2} = \pm\sqrt{49}
\]
Simplifying the square roots, we know that \(\sqrt{(x - 3)^2}=|x - 3|\), but for the purpose of solving this equation, we can also directly say that \(x - 3=\pm7\) (since if \(y^2 = a\) where \(a\geq0\), then \(y=\pm\sqrt{a}\)).

Step2: Solve for \(x\) in both cases

Case 1: \(x - 3 = 7\)

To solve for \(x\), we add 3 to both sides of the equation:
\[
x-3 + 3=7 + 3
\]
Simplifying both sides, we get:
\[
x = 10
\]

Case 2: \(x - 3=-7\)

Again, we add 3 to both sides of the equation:
\[
x-3 + 3=-7 + 3
\]
Simplifying both sides, we get:
\[
x=-4
\]

Answer:

-4, 10 (corresponding to the options: -4, 10)