Answer:
[tex]5(x^2+4x)=7[/tex]
[tex]5(x^2+4x+4)=7+20[/tex]
[tex](x+2)=\pm\sqrt{\frac{27}{5}}[/tex]
Step-by-step explanation:
we have
[tex]5x^2+20x-7=0[/tex]
step 1
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]5x^2+20x=7[/tex]
step 2
Factor 5 left side
[tex]5(x^2+4x)=7[/tex]
step 3
Complete the square
[tex]5(x^2+4x+2^2)=7+2^2(5)[/tex]
[tex]5(x^2+4x+4)=7+20[/tex]
[tex]5(x^2+4x+4)=27[/tex]
step 4
Rewrite as perfect squares
[tex]5(x+2)^2=27[/tex]
step 5
[tex](x+2)^2=\frac{27}{5}[/tex]
[tex](x+2)=\pm\sqrt{\frac{27}{5}}[/tex]
[tex](x+2)=\pm\frac{3\sqrt{15}}{5}[/tex]
step 6
[tex]x=-2\pm\frac{3\sqrt{15}}{5}[/tex]
