Chapter 9.6, Problem 7CYU

To determine

Solve the equation by using Quadratic formula.

Answer to Problem 7CYU

Solutions are $-6\text{and}\frac{1}{2}$

Explanation of Solution

Given:

The equation: $2x^2+11x-6=0$

Concept Used:

Solving the quadratic equation by using the quadratic formula:

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

Calculation:

Solving the quadratic equation by using the quadratic formula:

Quadratic equation: $2x^2+11x-6=0$

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ 2x^2+11x-6=0[\text{standard}\text{form}]\\ a=2;b=11;c=-6\\ x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-11\pm \sqrt{{(11)}^2-4·2·-6}}{2·2}1=\frac{-11\pm \sqrt{121+48}}{4}=\frac{-11\pm \sqrt{169}}{4}=\frac{-11\pm 13}{4}\\ x==\frac{-11+13}{4}\text{and}=\frac{-11-13}{4}\\ x=\frac{1}{2}\text{and}-6\\ x=\frac{1}{2}\text{and}x=-6\end{array}$

Solutions are $-6\text{and}\frac{1}{2}$

Thus, solutions are $-6\text{and}\frac{1}{2}$