Chapter 9, Problem 19PT

To determine

To solve equation by using Quadratic Formula.

Answer to Problem 19PT

  $x=8.2,1.8$

Explanation of Solution

Given information :

The function provided is $x^2-10x=-15$

Formula used :

To solve the equation using quadratic formula we need substitute values in the quadratic form given below. This can be found by using $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘ a’ , ‘ b’ and ‘ c’ are the co-efficient of the given equation.

Here, $a=1,b=-10\text{ and}c=15$

Calculation :

The given quadratic equation.

  $x^2-10x+15=0$

Putting the values in the formula.

  $x=\frac{-(-10)\pm \sqrt{{(-10)}^2-4\times 1\times (15)}}{2\times 1}$

Simplifying the expression.

  $x=\frac{10\pm \sqrt{100-60}}{2}$

Further simplification

  $x=\frac{10\pm \sqrt{40}}{2}$

Simplifying.

  $x=5\pm \sqrt{\frac{40}{4}}$

Removing the square root

  $x=5\pm 3.16$

First square root is

  $x=8.16$

Second square root is

  $x=1.84$

Therefore, $x=8.2,1.8$ .