Chapter 9, Problem 18PT

To determine

To solve equation by using Quadratic Formula.

Answer to Problem 18PT

  $x=6,-5$

Explanation of Solution

Given information :

The function provided is $x^2-x-30=0$

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, $a=1,b=-1\text{ and}c=-30$

Calculation :

The given quadratic equation.

  $x^2-x-30=0$

Putting the values in the formula.

  $x=\frac{-(-1)\pm \sqrt{{(-1)}^2-4\times 1\times (-30)}}{2\times 1}$

Simplifying the expression.

  $x=\frac{1\pm \sqrt{1+120}}{2}$

Further simplification

  $x=\frac{1\pm \sqrt{121}}{2}$

Removing the square root

  $x=\frac{1\pm 11}{2}$

First square root is

  $x=6$

Second square root is

  $x=-5$

Therefore, $x=6,-5$ .