Question

Which are solutions of x2 + 5x = 2? Check all that apply.

Answer 1

The last two are correct. So 4 and 5!

Answer 2

we have

$x^{2} +5x=2$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +5x+2.5^{2}=2+2.5^{2}$

$x^{2} +5x+6.25=2+6.25$

$x^{2} +5x+6.25=8.25$

Rewrite as perfect squares

$(x+2.5)^{2}=8.25$

Square Root both sides

$(x+2.5)=(+/-)\sqrt{8.25}$

$x=(+/-)\sqrt{8.25}-2.5$

$\sqrt{8.25}=\frac{\sqrt{33}}{2}$

substitute

$x=(+/-)\frac{\sqrt{33}}{2}-2.5$

therefore

the answer is

the solutions are

$x1=-2.5+\frac{\sqrt{33}}{2}$ or $x1=\frac{-5+\sqrt{33}}{2}$

$x2=-2.5-\frac{\sqrt{33}}{2}$ or $x2=\frac{-5-\sqrt{33}}{2}$