Chapter 9.4, Problem 31E

To determine

To solve the equation by complete the square for expression.

  $2x^2-14x+10=26$

Answer to Problem 31E

The solutions are $8$ and $-2$

Explanation of Solution

Given information:

Expression

  $2x^2-14x+10=26$

Calculation:

Original equation

  $2x^2-14x+10=26$

Subtract $10$ both sides

  $2x^2-14x=26-10$

Simplify

  $2x^2-14x=16$

Divide by 2 both sides

  $\frac{2x^2-14x}{2}=\frac{16}{2}$

Simplify

  $x^2-7x=8$

Since ${\left(\frac{7}{2}\right)}^2=\frac{49}{4}$ , add $\frac{49}{4}$ to both sides

  $x^2-7x+\frac{49}{4}=8+\frac{49}{4}$

Simplify

  $x^2-7x+\frac{49}{4}=\frac{81}{4}$

  $\frac{1}{4}\left(4x^2-28x+49\right)=\frac{81}{4}$

Simplify

  $\left(4x^2-28x+49\right)=81$

Factor $\left(4x^2-28x+49\right)$

  ${\left(2x-7\right)}^2=81$

On solving

  $2x-7=\pm 9$

Add $7$ both sides

  $2x=7\pm 9$

Divide by 2 both sides

  $x=\frac{7\pm 9}{2}$

Separating the equations

  $x=\frac{7+9}{2}$ Or $x=\frac{7-9}{2}$

On solving

  $x=8$ Or $x=-2$

The solutions are $8$ and $-2$