Sure, let's solve the equation step by step:
Given the equation:
[tex]\[
-4 + \sqrt{u + 6} = 6
\][/tex]
1. Isolate the square root term:
To isolate [tex]\(\sqrt{u + 6}\)[/tex], add 4 to both sides of the equation:
[tex]\[
-4 + \sqrt{u + 6} + 4 = 6 + 4
\][/tex]
Simplifying this, we get:
[tex]\[
\sqrt{u + 6} = 10
\][/tex]
2. Eliminate the square root:
Square both sides of the equation to get rid of the square root:
[tex]\[
(\sqrt{u + 6})^2 = 10^2
\][/tex]
Simplifying this, we have:
[tex]\[
u + 6 = 100
\][/tex]
3. Solve for [tex]\(u\)[/tex]:
Subtract 6 from both sides to solve for [tex]\(u\)[/tex]:
[tex]\[
u + 6 - 6 = 100 - 6
\][/tex]
Simplifying this, we get:
[tex]\[
u = 94
\][/tex]
Therefore, the solution to the equation [tex]\(-4 + \sqrt{u + 6} = 6\)[/tex] is:
[tex]\[
u = 94
\][/tex]
