Question

solve the equation for all values of x in simplest form:
$(x - 3)^2 = 16$

Explanation:

Step1: Take square root of both sides

To solve \((x - 3)^2 = 16\), 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 \(x - 3=\pm\sqrt{16}\).

Step2: Simplify the square root

We know that \(\sqrt{16} = 4\), so the equation becomes \(x - 3=\pm4\).

Step3: Solve for x in two cases

Case 1: When we take the positive root

If \(x - 3 = 4\), we add 3 to both sides of the equation. So \(x=4 + 3\), which gives \(x = 7\).

Case 2: When we take the negative root

If \(x - 3=-4\), we add 3 to both sides of the equation. So \(x=-4 + 3\), which gives \(x=-1\).

Answer:

\(x = 7\) or \(x=-1\)