Chapter 12.5, Problem 5WE

To determine

Solve the quadratic equation.

Answer to Problem 5WE

  $x=\frac{-7\pm \sqrt{41}}{2}$

Explanation of Solution

Given:

The equation is :

  $x^2+7x+2=0$

Calculation:

The given equation $x^2+7x+2=0$ is of the type $a{x}^2+bx+c=0$ , where a = 1 and b = 7, c = 2 .

  $b^2-4ac=7^2-4(1)(2)=49-8=41$ , which is not perfect square .

So, it can be solved by using the Quadratic Formula : $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So,

  $\begin{array}{l}x=\frac{-7\pm \sqrt{41}}{2(1)}\\ \Rightarrow x=\frac{-7\pm \sqrt{41}}{2}\end{array}$