Question

Solve the square root equation 7+2x−1−−−−−−√=10
7
+
2
𝑥
−
1
=
10
.(1 point)
The solution to the square root equation is x=
𝑥
=

Answer 1

To solve the equation \( \sqrt{7 + 2x - 1} = 10 \), let's first simplify the left side.

The equation can be rewritten as:

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

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

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

This simplifies to:

\[
6 + 2x = 100
\]

Now, we can isolate \(2x\) by subtracting 6 from both sides:

\[
2x = 100 - 6
\]

\[
2x = 94
\]

Next, divide both sides by 2 to solve for \(x\):

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

\[
x = 47
\]

Thus, the solution to the square root equation is:

\[
x = 47
\]