Chapter 1, Problem 23REAE

Solution

Solve the equation $3x^2-24x-48=0$ by factoring.

The solution for the equation is $x=\left\{4+4\sqrt{2},4-4\sqrt{2}\right\}$ .

Given:

The equation is $3x^2-24x-48=0$ .

Calculation:

Simplify the equation $3x^2-24x-48=0$ by factoring method.

  $\begin{array}{c}3x^2-24x-48=0\mathrm{......}\left(\text{Given}\right)\\ x^2-8x-16=0\mathrm{......}\left(\text{Divide both sides by }3\right)\\ \left(x^2-8x+16\right)-16=0+16\\ {\left(x-4\right)}^2-32=0\\ {\left(x-4\right)}^2-{\left(4\sqrt{2}\right)}^2=0\\ \left(x-4-4\sqrt{2}\right)\left(x-4+4\sqrt{2}\right)=0\\ x-4-4\sqrt{2}=0\text{or }x-4+4\sqrt{2}=0\\ x=4+4\sqrt{2}\text{or }x=4-4\sqrt{2}\\ x=\left\{4+4\sqrt{2},4-4\sqrt{2}\right\}\end{array}$

Conclusion:

Hence, the solution for the equation is $x=\left\{4+4\sqrt{2},4-4\sqrt{2}\right\}$ .