Chapter 9.6, Problem 8CYU

To determine

Solve the equation by using Quadratic formula.

Answer to Problem 8CYU

Solutions are $-1.1\text{and}2.6$

Explanation of Solution

Given:

The equation: $2x^2-3x-6=0$

Concept Used:

Solve 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:

Solve the quadratic equation by using the quadratic formula.

Quadratic equation: $2x^2-3x-6=0$

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ 2x^2-3x-6=0[\text{standard}\text{form}]\\ a=2;b=-3;c=-6\\ x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-(-3)\pm \sqrt{{(-3)}^2-4·2·-6}}{2·2}1=\frac{3\pm \sqrt{9+48}}{4}=\frac{3\pm \sqrt{57}}{4}=\frac{3\pm \sqrt{57}}{4}\\ x==\frac{3+7.5}{4}\text{and}=\frac{3-7.5}{4}\\ x=2.6\text{and}-1.1\\ x=2.6\text{and}x=-1.1\end{array}$

Solutions are $-1.1\text{and}2.6$

Thus, solutions are $-1.1\text{and}2.6$