Question

solving simple quadratic equations practice
complete this assessment to review what you’ve learned. it will not count toward your grade.
solve the following quadratic equation using square roots: ((x + 3)^2 = 36). (1 point)

Explanation:

Step1: Take square roots of both sides

To solve \((x + 3)^2=36\) using square roots, we take the square root of each side. Remember that when we take the square root of a number, we get both a positive and a negative solution. So, \(\sqrt{(x + 3)^2}=\pm\sqrt{36}\).

Simplifying both sides, we know that \(\sqrt{(x + 3)^2}=|x + 3|\), but since we are dealing with real numbers and we can consider the two cases (positive and negative square roots), we can write \(x + 3=\pm6\).

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

Case 1: When the square root is positive

If \(x + 3 = 6\), then we subtract 3 from both sides to solve for \(x\).
\(x=6 - 3\)
\(x = 3\)

Case 2: When the square root is negative

If \(x + 3=-6\), then we subtract 3 from both sides to solve for \(x\).
\(x=-6 - 3\)
\(x=-9\)

Answer:

The solutions are \(x = 3\) and \(x=-9\)