Question

Complete the square of 4 x squared plus 8X minus 5 equals 0

Answer 1

The answer to your question above  is 24x-5

Answer 2

First, subtract $-5$ from both sides:
$4{x}^{2}+8x=5$
Divide both sides by 4:
${x}^{2}+2x=\frac{5}{4}$
Add $({\frac{b}{2}})^{2}=({\frac{2}{2}})^{2}=1$ to both sides to complete the square:
${x}^{2}+2x+1=\frac{9}{4}$
${(x+1)}^{2}=\frac{9}{4}$
We now take the square root of both sides, getting two different equations:
$x+1=\frac{3}{2}$ or $x+1=-\frac{3}{2}$
Solving each, we get $\left \{ {{x_1=\frac{1}{2}} \atop {x_2=-\frac{5}{2}} \right.$