Chapter 9.6, Problem 10CYU

To determine

Solve the equation by using Quadratic formula.

Answer to Problem 10CYU

Solutions are $5.6\text{and}3.4$

Explanation of Solution

Given:

The equation: $x^2-9x=-19$

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: $x^2-9x=-19$

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x^2-9x=-19\\ x^2-9x+19=0[\text{standard}\text{form}]\\ a=1;b=-9;c=19\\ x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-(-9)\pm \sqrt{{(-9)}^2-4·1·19}}{2·1}1=\frac{9\pm \sqrt{81-76}}{2}=\frac{9\pm \sqrt{5}}{2}\\ x==\frac{9+\sqrt{5}}{2}\text{and}x=\frac{9-\sqrt{5}}{2}\\ x=5.6\text{and}x=3.4\end{array}$

Solutions are $5.6\text{and}3.4$

Thus, solutions are $5.6\text{and}3.4$