Chapter 9, Problem 51SGR

To determine

To compute the value of the equation using quadratic formula.

Answer to Problem 51SGR

The value of x is -2.5 and 1.5

Explanation of Solution

Given information :

The function provided is $4x^2+4x=15$ . This can be written as $4x^2+4x-15=0$ .

Formula used :

Quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . Here ‘a’, ‘b’ and ‘c’ are the co-efficient of the given equation.

Here, $a=4,b=4\text{ and}c=-15$ .

Calculation :

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

Putting the values in the formula.

  $x=\frac{-4\pm \sqrt{16+240}}{8}$

Simplifying

  $x=\frac{-4\pm \sqrt{256}}{8}$

Removing square root.

  $x=\frac{-4\pm 16}{8}$

The first root

  $x=\frac{-4-16}{8}$

Simplifying

  $x=-2.5$

This is the first root.

  $x=\frac{-4+16}{8}$

Second root

  $x=1.5$