Math help asap!!!!

Question

If using the method of completing the square to solve the quadratic equation x^2+13x+15=0, which number would have to be added to "complete the square"?

Answer 1

x² + 13x + 15 = 0

ax² + bx + c = 0

a = 1, b = 13, c = 15

Recall that a quadratic expression such as x² + 6x + 9 can be factored as (x+3)²

When quadratic expressions can be factored into a binomial squared such as (x+3)² we call them perfect square quadratics.

When completing the square we first move the constant to the other side of the equation

x²+13x = -15

Now our goal is to make the left side a perfect square quadratic. The constant (commonly referred to as the c value) needs to be (half the b value)² or in this case (13/2)² = 169/4. Thus, we need to add 169/4 to both sides of the equation.

x² + 13x + 169/4 = -15 + 169/4

x² + 13x + 169/4 = 109/4

You can now factor the left side as you have learned how to do previously but that's too much work. It will always factor to [x + (the value you just squared to get c)]² or in this case

x² + 13x + 169/4 factors to (x + 13/2)²

Therefore we can use that in the equation to write

(x + 13/2)² = 109/4

Now you have to square root both sides, remember something about a ±, and then perform some elementary algebra to get the two solutions to the equation.

Answer 2

x²+13x+15=0

Moving the 15 over, we get x²+13x=-15

Remember when completing the square, we want (b/2)² so this value would be (13/2)² or 169/4

169/4 is what we would want to add to both sides and solve

Hope this helped!

Answer 3

for x2 + 13x + 15 = 0 Remember when completing the square, you take the x term and divide by 2

Then

(x + 13/2)² + 15 = the squared constant term which is (13/2)² = 169/4

So,

(x + 13/2)² = 169/4 - 60/4 = 109/4

Therefore;

x +13/2 = (1/2)sqrt(109) or x = -13/2 +- (1/2)sqrt(109)