Chapter 9.4, Problem 34E

To determine

To describe and correct the error in solve the equation by complete the square for expression.

  $2x^2-2x-4=0$

Answer to Problem 34E

The solutions are $2$ and $-1$

Explanation of Solution

Given information:

Expression

  $2x^2-2x-4=0$

Calculation:

Original equation

  $2x^2-2x-4=0$

Here is error added 4 both sides instead of divided by $2$ both sides

Divide by $2$ both sides

  $\frac{2x^2-2x-4}{2}=\frac{0}{2}$

On solving

  $x^2-x-2=0$

Here is error added 1 both sides instead of add $2$ both sides

Add $2$ both sides

  $x^2-x=2$

Since ${\left(\frac{-1}{2}\right)}^2=\frac{1}{4}$ , add $\frac{1}{4}$ to both sides

  $x^2-x+\frac{1}{4}=2+\frac{1}{4}$

On solving

  $\frac{1}{4}\left(4x^2-4x+1\right)=\frac{9}{4}$

On solving

  $\left(4x^2-4x+1\right)=9$

Factor $\left(4x^2-4x+1\right)$

  ${\left(2x-1\right)}^2=9$

On solving

  $\left(2x-1\right)=\pm 3$

Add $1$ both sides

  $2x=1\pm 3$

Divide by $2$ both sides

  $x=\frac{1\pm 3}{2}$

Separating the equations

  $x=\frac{1+3}{2}$ Or $x=\frac{1-3}{2}$

On solving

  $x=2$ Or $x=-1$

The solutions are $2$ and $-1$