Chapter ISG, Problem 9.9.1.2P

To determine

To solve equation.

Answer to Problem 9.9.1.2P

  $x_1\approx -0.93$

  $x\approx 5.53$

Explanation of Solution

Given information:

  $-0.8+3.1=x^2-5.4x-2.1$

Calculation:

  $-0.8+3.1=x^2-5.4x-2.1$

Convert decimals to fractions

  $-\frac{4}{5}+\frac{31}{10}=x^2-\frac{27}{5}x-\frac{21}{10}$

Multiply both side by 10

  $-8x+31=10x^2-54x-21$

Move expression to left

  $-8x+31-10x^2+54x+21=0$

Collect like terms

  $46x+52-10x^2=0$

Reordered the terms

  $-10x^2+46x+52=0$

Divide both side by -2

  $5x^2-23x-26=0$

Solve quadratic equations

  $x=\frac{-(-23)\pm \sqrt{{(-23)}^2-4(5)(-26)}}{2(5)}$

Remove parentheses

  $x=\frac{23\pm \sqrt{529+520}}{10}$

Add numbers

  $x=\frac{23\pm \sqrt{1049}}{10}$

Separate the solutions

  $x=\frac{23\pm \sqrt{1049}}{10}$

  $x=\frac{23-\sqrt{1049}}{10}$

The final solutions are

  $x_1\approx -0.93$

  $x\approx 5.53$