Question

Solve each of the following equations by using the method of completing the square:
$2x^2+5x-3=0$

Answer 1

$2x^2+5x-3=02x^2+5x=3x^2+\frac{5}{2}x=\frac{3}{2}{x}^2+\frac{5}{2}x+(\frac{5}{4}{)}^2=\frac{3}{2}+(\frac{5}{4}{)}^2(x+\frac{5}{2}{)}^2=\frac{3}{2}+\frac{25}{4}=\frac{12+50}{8}=\frac{62}{8}=\frac{31}{4}x+\frac{5}{2}=\sqrt{\frac{31}{4}}=\pm \frac{\sqrt{31}}{2}x=\pm \frac{\sqrt{31}}{2}-\frac{5}{2}x=\frac{\sqrt{31}}{2}-\frac{5}{2}or\frac{-\sqrt{31}}{2}-\frac{5}{2}x=\frac{\sqrt{31}-5}{2}or\frac{-\sqrt{31}-5}{2}$