Question

In the following exercises, solve by completing the square.

$5x^2+20x=15$

Short answer

The solution is$x=-2-\sqrt{7},x=-2+\sqrt{7}$

Step-by-step solution

Step 1. Given information 

Equation:$5x^2+20x=15$

Step 2. Calculation   

We have,

$5x^2+20x=15$

$5\left(x^2+4x\right)=5\left(3\right)$

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

$x^2+4x=3$

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

$x^2+4x+{\left(2\right)}^2=3+{\left(2\right)}^2$

$x^2+4x+4=3+4$

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

$\sqrt{{\left(x+2\right)}^2}=\sqrt{7}$

$x+2=\pm \sqrt{7}$

$x+2-2=-2-\sqrt{7},x+2-2=-2+\sqrt{7}$

$x=-2-\sqrt{7},x=-2+\sqrt{7}$