Answer:
The steps used in solving from options are
[tex]8(x^{2}+2x)=-3\\8(x^{2}+2x+1)=-3+8[/tex]
Step-by-step explanation:
Given : Quadratic equation [tex]8x^2+16x+3=0[/tex]
To find : Which steps could he use to solve the quadratic equation?
Solution :
Quadratic equation [tex]8x^2+16x+3=0[/tex]
Step 1 - Take constant to another side,
[tex]8x^2+16x=-3[/tex]
Step 2 - Take 8 common from LHS,
[tex]8(x^2+2x)=-3[/tex]
Step 3 - Completing the square by adding and subtracting square of 1 inside the bracket,
[tex]8(x^2+2x+1)=-3+8[/tex]
[tex]8(x^2+2x+1)=5[/tex]
Step 4 - Write as perfect square,
[tex]8(x+1)^2=5[/tex]
[tex](x+1)^2=\frac{5}{8}[/tex]
Taking root both side,
[tex]\sqrt{(x+1)^2}=\sqrt{\frac{5}{8}}[/tex]
[tex]x+1=\pm 0.79[/tex]
[tex]x_1=0.79-1=-0.21[/tex]
[tex]x_1=-0.79-1=-1.79[/tex]
Therefore, The steps used in solving from options are
[tex]8(x^{2}+2x)=-3\\8(x^{2}+2x+1)=-3+8[/tex]
