Question

Solve for x
10+square root of 10x-1=13

Answer 1

To solve the equation \( 10 + \sqrt{10x - 1} = 13 \), follow these steps:

1. Subtract 10 from both sides of the equation:

\[
\sqrt{10x - 1} = 13 - 10
\]
\[
\sqrt{10x - 1} = 3
\]

2. Square both sides to eliminate the square root:

\[
(\sqrt{10x - 1})^2 = 3^2
\]
\[
10x - 1 = 9
\]

3. Add 1 to both sides:

\[
10x = 9 + 1
\]
\[
10x = 10
\]

4. Divide by 10:

\[
x = \frac{10}{10}
\]
\[
x = 1
\]

Now, let's verify the solution:

Substituting \( x = 1 \) back into the original equation:

\[
10 + \sqrt{10(1) - 1} = 10 + \sqrt{10 - 1} = 10 + \sqrt{9} = 10 + 3 = 13
\]

The equation holds true, so the solution is:

\[
\boxed{1}
\]