Question

In the following exercises, solve by completing the square.

$2x^2+7x-15=0$

Short answer

The solution is$x=-5,x=\frac{3}{2}$

Step-by-step solution

Step 1. Given information 

Equation:$2x^2+7x-15=0$

Step 2. Calculation    

We have,

$2x^2+7x-15=0$

$2x^2+7x-15+15=0+15$

$\frac{2x^2+7x}{2}=\frac{15}{2}$

role="math" localid="1645178124973" $x^2+\frac{7x}{2}+{\left(\frac{1}{2}·\left(\frac{7}{2}\right)\right)}^2=\frac{15}{2}+{\left(\frac{1}{2}·\left(\frac{7}{2}\right)\right)}^2$

$x^2+\frac{7x}{2}+{\left(\frac{7}{4}\right)}^2=\frac{15}{2}+{\left(\frac{7}{4}\right)}^2$

$x^2+\frac{7x}{2}+\frac{49}{16}=\frac{15}{2}+\frac{49}{16}$

${\left(x+\frac{7}{4}\right)}^2=\frac{169}{16}$

$\sqrt{{\left(x+\frac{7}{4}\right)}^2}=\sqrt{\frac{169}{16}}$

$x+\frac{7}{4}=\pm \frac{13}{4}$

$x+\frac{7}{4}-\frac{7}{4}=-\frac{13}{4}-\frac{7}{4},x+\frac{7}{4}-\frac{7}{4}=\frac{13}{4}-\frac{7}{4}$

$x=-\frac{20}{4},x=\frac{6}{4}$

$x=-5,x=\frac{3}{2}$