Answer :
To solve the equation [tex]\(\sqrt{4x + 61} + 15 = 22\)[/tex], follow these steps:
1. Isolate the Square Root Term:
Start by subtracting 15 from both sides of the equation:
[tex]\[
\sqrt{4x + 61} = 22 - 15
\][/tex]
[tex]\[
\sqrt{4x + 61} = 7
\][/tex]
2. Eliminate the Square Root:
Square both sides of the equation to get rid of the square root:
[tex]\[
(\sqrt{4x + 61})^2 = 7^2
\][/tex]
[tex]\[
4x + 61 = 49
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Next, subtract 61 from both sides to solve for [tex]\(4x\)[/tex]:
[tex]\[
4x = 49 - 61
\][/tex]
[tex]\[
4x = -12
\][/tex]
Finally, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-12}{4}
\][/tex]
[tex]\[
x = -3
\][/tex]
The solution to the equation is [tex]\(x = -3\)[/tex].
1. Isolate the Square Root Term:
Start by subtracting 15 from both sides of the equation:
[tex]\[
\sqrt{4x + 61} = 22 - 15
\][/tex]
[tex]\[
\sqrt{4x + 61} = 7
\][/tex]
2. Eliminate the Square Root:
Square both sides of the equation to get rid of the square root:
[tex]\[
(\sqrt{4x + 61})^2 = 7^2
\][/tex]
[tex]\[
4x + 61 = 49
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Next, subtract 61 from both sides to solve for [tex]\(4x\)[/tex]:
[tex]\[
4x = 49 - 61
\][/tex]
[tex]\[
4x = -12
\][/tex]
Finally, divide both sides by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-12}{4}
\][/tex]
[tex]\[
x = -3
\][/tex]
The solution to the equation is [tex]\(x = -3\)[/tex].
