Question

(Giving 25 points since I need help asap.) Solve the quadratic equation by completing the square. You MUST use this method for credit.

(from lesson 5.03 – 4 points)



x^2 + 14x − 51 = 0

What should you add to both sides to complete the square? _________

Solution(s): _____________

Answer 1

x = -17, x = 3, and you should add 100

Explanation:

When completing the square, I like to follow a specific method.

First, I take the b-value and divide it by 2. This gives us to, in this situation, 7.

This means that the inside value in the (x-h)^2 area will be (x+7)^2

Now we find the square of that number, so 7^2 = 49. Now we have to find the distance between the number squared and the number on the outside. So we have to find the total distance between 49 and -51. To do this, we simply add 49 to 51, and we get 100, and then we set it as a negative.

We end up with (x+7)^2 - 100. On both sides, you should add 100.

Using the quadratic formula, the solutions are also x = -17, and x =3