Question

Which of the following is the result of the equation below after completingthe square and factoring?X2+3x+8 = 6O A. (x+2) = -2OB. (x+ 2 - 1OC. (x+3)2 = -2D. (x+3) = 1

Answer 1

Problem:

Which of the following is the result of the equation below after completing the square and factoring?

$x^2+3x+8=6$

Solution:

To complete the square of the polynomial

$ax^2+bx+c=d$

we add to both sides of the above equation the fraction:

$(\frac{b}{2a})^2$

in our case we have that a = 1, b = 3, c = 8 and d = 6 .Then we have that:

$(\frac{b}{2a})^2=\text{ }(\frac{3}{2})^2\text{ }$

adding the above number on both sides of the given polynomial, we obtain:

$x^2+3x+(\frac{3}{2})^2+8=6+(\frac{3}{2})^2$

this is equivalent to:

$x^2+3x+(\frac{3}{2})^2=6+(\frac{3}{2})^2-8$

then we have:

$(x^{}+\frac{3}{2})^2=\frac{1}{4}$