Question

use the square root property to solve the quadratic equation.$2x^2=5$choose the correct answer below and, if necessary, fill in the answer box to complete your choicea. 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 $x^2$

Divide both sides by 2:
$\frac{2x^2}{2} = \frac{5}{2}$
$x^2 = \frac{5}{2}$

Step2: Apply square root property

Take square root of both sides:
$x = \pm\sqrt{\frac{5}{2}}$

Step3: Simplify the radical

Rationalize the denominator:
$x = \pm\frac{\sqrt{5}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \pm\frac{\sqrt{10}}{2}$

Answer:

A. The real solution(s) is/are $x = \frac{\sqrt{10}}{2}, -\frac{\sqrt{10}}{2}$