Question

In the following exercises, solve by completing the square.

$3d^2-4d=15$

Short answer

The solution is$d=-\frac{5}{3},d=3$

Step-by-step solution

Step 1. Given information 

Equation:$3d^2-4d=15$

Step 2. Calculation   

We have,

$3d^2-4d=15$

$\frac{3d^2-4d}{3}=\frac{15}{3}$

$d^2-\frac{4d}{3}=5$

$d^2-\frac{4d}{3}+{\left(\frac{1}{2}·\left(-\frac{4}{3}\right)\right)}^2=5+{\left(\frac{1}{2}·\left(-\frac{4}{3}\right)\right)}^2$

$d^2-\frac{4d}{3}+{\left(-\frac{2}{3}\right)}^2=5+{\left(-\frac{2}{3}\right)}^2$

$d^2-\frac{4d}{3}+\frac{4}{9}=5+\frac{4}{9}$

${\left(d-\frac{2}{3}\right)}^2=\frac{49}{9}$

$\sqrt{{\left(d-\frac{2}{3}\right)}^2}=\sqrt{\frac{49}{9}}$

$d-\frac{2}{3}=\pm \frac{7}{3}$

$d-\frac{2}{3}+\frac{2}{3}=-\frac{7}{3}+\frac{2}{3},d-\frac{2}{3}+\frac{2}{3}=\frac{7}{3}+\frac{2}{3}$

$d=-\frac{5}{3},d=\frac{9}{3}$

$d=-\frac{5}{3},d=3$