Chapter 11.9, Problem 11MRE

To determine

Simplify the given equation.

Answer to Problem 11MRE

  $\boxed{x=9,x=5}$

Explanation of Solution

Given information:

  $x^2-14x+45=0$

Formula used:

Quadratic roots formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where $x$ is the root of the quadratic equation $a{x}^2+bx+c=0$

Now finding the roots of the quadratic equation $x^2-14x+45=0$ with the help of $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ :

  $x^2-14x+45=0$ , Here $a=1,b=-14,c=45$

  $\begin{array}{l}x=\frac{-\left(-14\right)\pm \sqrt{{\left(-14\right)}^2-4\left(1\right)\left(45\right)}}{2\left(1\right)}\\ x=\frac{14\pm \sqrt{196-180}}{2}\\ x=\frac{14\pm \sqrt{16}}{2}\\ x=\frac{14\pm 4}{2}\end{array}$

  $\begin{array}{l}x=\frac{18}{2},x=\frac{10}{2}\\ \boxed{x=9,x=5}\end{array}$