Chapter 9.6, Problem 9CYU

To determine

Solve the quadratic equation by factoring.

Answer to Problem 9CYU

Solutions are: $-\frac{5}{3}\text{and}\frac{5}{3}$

Explanation of Solution

Given:

The equation:

Concept Used:

Solve the quadratic equation by factoring.

Rule of difference of square: $a^2-b^2=(a+b)(a-b)$

Calculation:

Solve the quadratic equation by factoring.

Rule of difference of square: $a^2-b^2=(a+b)(a-b)$

  $\begin{array}{l}\text{Equation:}9x^2=25\\ 9x^2-25=0[\text{Standard}\text{Form}]\\ \text{Factoring}:9x^2-25=0\\ $ {(3x)}^2-{(5)}^2=0$(3x+5)(3x-5)[\text{Rule}:a^2-b^2=(a+b)(a-b)]\\ 3x+5=0\text{and}3x-5=0\\ x=-\frac{5}{3}\text{and}x=\frac{5}{3}\end{array}$

Solutions are: $-\frac{5}{3}\text{and}\frac{5}{3}$

Thus, solutions are: $-\frac{5}{3}\text{and}\frac{5}{3}$