Chapter 9.6, Problem 2CYU

To determine

Solve the equation by using Quadratic formula.

Answer to Problem 2CYU

Solutions are $8\text{and}2$

Explanation of Solution

Given:

The equation: $x^2-10x+16=0$

Concept Used:

Quadratic equation: $a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Quadratic equation: $x^2-10x+16=0$

  $\begin{array}{l}\text{The}\text{quadratic}\text{equation}:a{x}^2+bx+c=0,\text{then}x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x^2-10x+16=0\\ a=1;b=-10;c=16\\ x=\frac{b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-(-10)\pm \sqrt{{(-10)}^2-4·1·16}}{2·1}1=\frac{10\pm \sqrt{100-64}}{2}=\frac{10\pm \sqrt{36}}{2}=\frac{10\pm 6}{2}\\ x=\frac{10+6}{2}\text{and}\frac{10-6}{2}\\ x=\frac{16}{2}\text{and}\frac{4}{2}\\ x=8\text{and}x=2\end{array}$

Solutions are $8\text{and}2$

Thus, solutions are $8\text{and}2$