Sure, let's solve the equation [tex]\(-10 \sqrt{v - 10} = 60\)[/tex] step-by-step.
1. Isolate the square root term:
First, divide both sides of the equation by [tex]\(-10\)[/tex] to isolate the square root.
[tex]\[
\frac{-10 \sqrt{v - 10}}{-10} = \frac{60}{-10}
\][/tex]
Simplifying, we get:
[tex]\[
\sqrt{v - 10} = -6
\][/tex]
2. Remove the negative sign:
Multiply both sides by [tex]\(-1\)[/tex] to get rid of the negative sign.
[tex]\[
\sqrt{v - 10} = 6
\][/tex]
3. Square both sides:
To eliminate the square root, square both sides of the equation.
[tex]\[
(\sqrt{v - 10})^2 = 6^2
\][/tex]
This simplifies to:
[tex]\[
v - 10 = 36
\][/tex]
4. Solve for [tex]\(v\)[/tex]:
Finally, add [tex]\(10\)[/tex] to both sides of the equation to solve for [tex]\(v\)[/tex].
[tex]\[
v - 10 + 10 = 36 + 10
\][/tex]
Simplifying, we get:
[tex]\[
v = 46
\][/tex]
Therefore, the solution to the equation [tex]\(-10 \sqrt{v - 10} = 60\)[/tex] is [tex]\(v = 46\)[/tex].
