Question

Solve the square root equation
√
32
−
4
x
−
x
+
1
=
1
.(1 point)


The solution to the square root equation is
x

=

Answer 1

To solve the equation

\[
\sqrt{32 - 4x - x + 1} = 1,
\]

let's first simplify the expression inside the square root:

\[
32 - 4x - x + 1 = 32 + 1 - 4x - x = 33 - 5x.
\]

Now, we can rewrite the equation as:

\[
\sqrt{33 - 5x} = 1.
\]

To eliminate the square root, we square both sides:

\[
33 - 5x = 1.
\]

Next, we solve for \(x\). Start by isolating the term with \(x\):

\[
33 - 1 = 5x,
\]
\[
32 = 5x.
\]

Now, divide both sides by 5:

\[
x = \frac{32}{5}.
\]

So, the solution to the square root equation is:

\[
x = \frac{32}{5}.
\]