we have
[tex]x^{2} +5x=2[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2} +5x+2.5^{2}=2+2.5^{2}[/tex]
[tex]x^{2} +5x+6.25=2+6.25[/tex]
[tex]x^{2} +5x+6.25=8.25[/tex]
Rewrite as perfect squares
[tex](x+2.5)^{2}=8.25[/tex]
Square Root both sides
[tex](x+2.5)=(+/-)\sqrt{8.25}[/tex]
[tex]x=(+/-)\sqrt{8.25}-2.5[/tex]
[tex]\sqrt{8.25}=\frac{\sqrt{33}}{2}[/tex]
substitute
[tex]x=(+/-)\frac{\sqrt{33}}{2}-2.5[/tex]
therefore
the answer is
the solutions are
[tex]x1=-2.5+\frac{\sqrt{33}}{2}[/tex] or [tex]x1=\frac{-5+\sqrt{33}}{2}[/tex]
[tex]x2=-2.5-\frac{\sqrt{33}}{2}[/tex] or [tex]x2=\frac{-5-\sqrt{33}}{2}[/tex]
