To solve the equation [tex]\(\sqrt{45 - 9x} - 6 = 0\)[/tex], we can follow a step-by-step process:
1. Isolate the square root term:
The equation is:
[tex]\[
\sqrt{45 - 9x} - 6 = 0
\][/tex]
Add 6 to both sides of the equation to isolate the square root term:
[tex]\[
\sqrt{45 - 9x} = 6
\][/tex]
2. Square both sides:
To eliminate the square root, square both sides of the equation:
[tex]\[
(\sqrt{45 - 9x})^2 = 6^2
\][/tex]
This simplifies to:
[tex]\[
45 - 9x = 36
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Isolate [tex]\(x\)[/tex] by first subtracting 45 from both sides:
[tex]\[
45 - 9x - 45 = 36 - 45
\][/tex]
Simplify the equation:
[tex]\[
-9x = -9
\][/tex]
Now, divide both sides by -9 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-9}{-9}
\][/tex]
Simplifying the fraction gives:
[tex]\[
x = 1
\][/tex]
4. Verify the solution:
Substitute [tex]\(x = 1\)[/tex] back into the original equation to check if it satisfies the equation:
[tex]\[
\sqrt{45 - 9(1)} - 6 = 0
\][/tex]
Simplify inside the square root:
[tex]\[
\sqrt{45 - 9} - 6 = 0
\][/tex]
Further simplify:
[tex]\[
\sqrt{36} - 6 = 0
\][/tex]
Since [tex]\(\sqrt{36} = 6\)[/tex]:
[tex]\[
6 - 6 = 0
\][/tex]
This simplifies to:
[tex]\[
0 = 0
\][/tex]
The equation holds true.
Therefore, the solution to the equation [tex]\(\sqrt{45 - 9x} - 6 = 0\)[/tex] is:
[tex]\[
x = 1
\][/tex]
