Question

(x - 4)^2 + 5 = 39

Explanation:

Step1: Subtract 3 from both sides

To isolate the squared term, we subtract 3 from each side of the equation \((x - 4)^2 + 3 = 39\). This gives us \((x - 4)^2 = 39 - 3\), which simplifies to \((x - 4)^2 = 36\).

Step2: Take square roots on both sides

Taking the square root of both sides, we get \(x - 4 = \pm\sqrt{36}\). Since \(\sqrt{36} = 6\), this becomes \(x - 4 = \pm 6\).

Step3: Solve for x in two cases

Case 1: When \(x - 4 = 6\)

Adding 4 to both sides, we have \(x = 6 + 4\), so \(x = 10\).

Case 2: When \(x - 4 = -6\)

Adding 4 to both sides, we get \(x = -6 + 4\), so \(x = -2\).

Answer:

The solutions are \(x = 10\) and \(x = -2\)