Question

Solve the square root equation 7+2x−1−−−−−−√=10
7
+
2
𝑥
−
1
=
10

Answer 1

To solve the equation

\[
\sqrt{7 + 2x - 1} = 10,
\]

we can first simplify the expression inside the square root:

\[
7 + 2x - 1 = 6 + 2x.
\]

Now the equation becomes:

\[
\sqrt{6 + 2x} = 10.
\]

Next, we square both sides to eliminate the square root:

\[
6 + 2x = 10^2.
\]

Calculating \(10^2\):

\[
6 + 2x = 100.
\]

Now, we can solve for \(x\). First, subtract 6 from both sides:

\[
2x = 100 - 6,
\]

which simplifies to:

\[
2x = 94.
\]

Now, divide both sides by 2:

\[
x = \frac{94}{2} = 47.
\]

Thus, the solution to the equation is:

\[
\boxed{47}.
\]

Finally, let's verify our solution by substituting \(x = 47\) back into the original equation:

We need to check if:

\[
\sqrt{7 + 2(47) - 1} = 10.
\]

Calculating the left side:

\[
\sqrt{7 + 94 - 1} = \sqrt{100}.
\]

Since \(\sqrt{100} = 10\), our solution is verified.

The final answer is:

\[
\boxed{47}.
\]