Question

What equation results from completing the square and then factoring? x^2 + 24x = 33

Answer 1

Answer:

$(x+12)^2=177$

Step-by-step explanation:

We have been given an equation: $x^2+24x=33$.

To complete the square we change the left hand side of the equation to a perfect square trinomial. For this we add $(\frac{b}{2})^2$ to both sides of equation, where b is the coefficient of x.

We can see that coefficient of x for our given equation is 24. So we will add $(\frac{24}{2})^2=12^2=144$ to both sides of our equation.

$x^2+24x+144=33+144$

$x^2+24x+144=177$

Let us factor left side of our equation as the square of  binomial.

$(x+12)^2=177$

Therefore, our resulting equation will be $(x+12)^2=177$.

Answer 2

  x^2+22x = 31 
x^2 + 22x + (22/2)^2 = 31 + (22/2)^2 
x^2 + 22x + 11^2 = 152 
(x + 11)^2 = 152 (D)