Question

solving simple quadratic equations practice
complete this assessment to review what youve learned. it will not count toward your grade.
solve the following quadratic equation using square roots. write your answer in set notation.
$(x - 6)^2 = 49$
(1 point)

Explanation:

Step1: Take square roots of both sides

To solve \((x - 6)^2 = 49\), 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:
\[
\sqrt{(x - 6)^2}=\pm\sqrt{49}
\]
Simplifying the square roots, we know that \(\sqrt{(x - 6)^2}=|x - 6|\), but since we are dealing with real numbers and we will consider both positive and negative roots, we can also write it as \(x - 6=\pm7\).

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

Case 1: When the right - hand side is positive

If \(x - 6 = 7\), then we add 6 to both sides of the equation to solve for \(x\):
\[
x=7 + 6=13
\]

Case 2: When the right - hand side is negative

If \(x - 6=-7\), then we add 6 to both sides of the equation:
\[
x=-7 + 6=-1
\]

Step3: Write the solution in set notation

The solutions of the equation are \(x = 13\) and \(x=-1\). In set notation, the solution set is \(\{-1,13\}\).

Answer:

\(\{-1, 13\}\)