Question

use the square root property to solve the quadratic equation.
$5x^2 = 11$
choose the correct answer below and, if necessary, fill in the answer box to complete your choice
a. the real solution(s) is/are x =
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)
b. there is no real solution.

Explanation:

Step1: Isolate $x^2$ term

Divide both sides by 5:
$\frac{5x^2}{5} = \frac{11}{5}$
Simplify to get:
$x^2 = \frac{11}{5}$

Step2: Apply square root property

Take square root of both sides:
$x = \pm\sqrt{\frac{11}{5}}$

Step3: Rationalize the denominator

Rewrite radical to rationalize:
$x = \pm\frac{\sqrt{11}}{\sqrt{5}} = \pm\frac{\sqrt{11} \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \pm\frac{\sqrt{55}}{5}$

Answer:

A. The real solution(s) is/are $x = \frac{\sqrt{55}}{5}, -\frac{\sqrt{55}}{5}$