Chapter 9.6, Problem 6CYU

To determine

Solve the equation by using Quadratic formula.

Answer to Problem 6CYU

Solutions are $-2.1\text{and}-0.5$

Explanation of Solution

Given:

The equation: $5x^2+5=-13x$

Concept Used:

Quadratic equation: $a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Quadratic equation: $5x^2+5=-13x$

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ 5x^2+5=-13x\\ 5x^2+13x+5=0[\text{standard}\text{form}]\\ a=5;b=13;c=5\\ x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-13\pm \sqrt{{(13)}^2-4·5·5}}{2·5}1=\frac{-13\pm \sqrt{169-100}}{10}=\frac{-13\pm \sqrt{69}}{10}\\ x==\frac{-13+\sqrt{69}}{10}\text{and}=\frac{-13-\sqrt{69}}{10}\\ x=-0.5\text{and}-2.1\\ x=-0.5\text{and}x=-2.1\end{array}$

Solutions are $-2.1\text{and}-0.5$

Thus, solutions are $-2.1\text{and}-0.5$