Chapter 12.6, Problem 75MR

To determine

To solve: The equation using quadratic formula.

Answer to Problem 75MR

The value of x is $0.807\text{ and}-\mathrm{6.807.}$

Explanation of Solution

Given information:

  $2x^2+12x-11=0$

Formula used:

If $a{x}^2+bx+c=0,\text{ and }a\ne 0,\text{ then}$

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Consider ,

  $2x^2+12x-11=0$

Here,

  $a=2,b=12,c=-11$

Therefore,

  $\begin{array}{l}x=\frac{-12\pm \sqrt{{\left(12\right)}^2-4\left(2\right)\left(-11\right)}}{2\left(2\right)}\\ =\frac{-12\pm \sqrt{144+88}}{4}\\ =\frac{-12\pm \sqrt{232}}{4}\\ =\frac{-12\pm 15.23154621}{4}\end{array}$

The value of x is

  $\begin{array}{l}=\frac{-12+15.2315}{4}\\ =\frac{3.2315}{4}\\ =0.807875\end{array}$ or $\begin{array}{l}=\frac{-12-15.2315}{4}\\ =-\frac{27.2315}{4}\\ =-6.807875\end{array}$

Hence, the value of x is $0.807\text{ and}-\mathrm{6.807.}$