Chapter P.5, Problem 7E

Solution

To solve the equation by extracting square roots $4x^2=25$ .

  $x=(+\frac{5}{2}),(-\frac{5}{2})$

Given:

The equation is, $4x^2=25$

Concept Used:

• Express the quadratic equation in standard form.
• Isolating the square and then applying the square root property.
• Include “±” when taking the square root of both sides.
• Solve the resulting linear equations.

Calculation:

  $\begin{array}{c}4x^2=25\\ x^2=\frac{25}{4}\\ \sqrt{x^2}=\sqrt{\frac{25}{4}}\\ x=\pm \frac{5}{2}\\ x=(+\frac{5}{2}),(-\frac{5}{2})\end{array}$

Thus, square roots of the given equation is $x=(+\frac{5}{2}),(-\frac{5}{2})$ .