Answer:
The answer is C. x=-4±[tex]2*\sqrt{5}[/tex]
Step-by-step explanation:
In order to determine the answer, we have to know some rules about the square of a binomial. it will help us to understand what we need to use the method of completing the square.
In general, a square of a binomial is:
[tex](a+b)^2=a^2+2*a*b+b^2[/tex]
- First term of the addition is the square of the first term of the binomial.
- Middle term of the addition is twice the product of the first term and the second term of the binomial.
- Last term of the addition is the square of the second term of the binomial.
So, in this case, we have the right side of the general equation and we need to get to the left side.
[tex]2x^2+16x-8=0\\x^2+8x-4=0\\x^2+8x=4[/tex]
Then, we need the last term of the addition in the left side of the equation. The term is 16 because its square root is 4 and:
[tex]2*x*4=8x[/tex]
So,
[tex]x^2+8x+16=4+16\\(x+4)^2=20\\\sqrt{(x+4)^2}=\sqrt{20}\\ x+4=\sqrt{20}\\ x=\sqrt{20}-4\\x=-4+\sqrt{5*4}\\x=-4+2*\sqrt{5}[/tex]
Finally, the solve is C. x=-4±[tex]2*\sqrt{5}[/tex]
