Chapter 9.3, Problem 17E

To determine

To solve: The equation $4x^2+10=11$ using square roots.

Answer to Problem 17E

The required solutions are $x=\frac{1}{2}$ and $x=-\frac{1}{2}$ .

Explanation of Solution

Given information:

The given equation $4x^2+10=11$

Calculation:

  $\begin{array}{l}4x^2+10=11\\ 4x^2=1\end{array}$

(Subtract 10 from each side)

  $x^2=\frac{1}{4}$

(Divide each side by 4)

  $x=\pm \sqrt{\frac{1}{4}}$

(Take the square root of each side)

  $x=\pm \frac{1}{2}$

(Simplify)

The solutions are $x=\frac{1}{2}$ and $x=-\frac{1}{2}$ .