College

Solve for [tex]x[/tex]:

[tex]
\sqrt{4x + 61} + 15 = 22
[/tex]

[tex]
-15
[/tex]

[tex]
4x + 61 = 7
[/tex]

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].