Chapter 12.3, Problem 17WE

To determine

To solve: the equation $3x^2+8x=2$ using quadratic formula. Give irrational roots in simplest radical form and then approximate them to the nearest tenth.

Answer to Problem 17WE

The required answer is: solution set is 2.9, - 0.23

Explanation of Solution

Given information:

The given equation: $3x^2+8x=2$

Calculation:

  $\begin{array}{l}3x^2+8x=2\\ 3x^2+8x-2=2-2\end{array}$

(Subtract 2 from both sides)

  $3x^2+8x-2=0$

(Simplify)

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

(Quadratic formula)

Where $a=3,b=8andc=-2$

  $x=\frac{-(8)\pm \sqrt{{(8)}^2-4(3)(-2)}}{2(3)}$

(Removing the brackets)

  $\begin{array}{l}=\frac{-8\pm \sqrt{64+24}}{6}\\ =\frac{-8\pm \sqrt{88}}{6}\\ =\frac{-8\pm \sqrt{4\cdot 22}}{6}\end{array}$

(Product property of square roots)

  $\begin{array}{l}=\frac{-8\pm 2\sqrt{22}}{6}\\ =\frac{2(-4\pm \sqrt{22})}{6}\end{array}$

(Distributive property)

  $=\frac{4\pm \sqrt{22}}{3}$

(Simplify)

Since $\sqrt{22}\approx 4.69$ , $x\approx \frac{4+4.69}{3}=\frac{8.69}{3}\approx 2.9$

Or     $x\approx \frac{4-4.69}{3}=\frac{-0.69}{3}\approx -0.23$

Therefore the solution set is $\frac{4+\sqrt{22}}{3},\frac{4-\sqrt{22}}{3}$ or 2.9, - 0.23