Question

If using the method of completing the square to solve the quadratic equation x, squared, minus, 15, x, minus, 10, equals, 0x 2 −15x−10=0, which number would have to be added to "complete the square"?

Answer 1

To complete the square, we need to add a constant term that will make the quadratic equation a perfect square trinomial. In this case, the constant terms that need to be added are ±7.5.

Step-by-step explanation:

To complete the square, we need to add a constant term that will make the quadratic equation a perfect square trinomial. In this case, the quadratic equation is x^2 - 15x - 10 = 0. To determine the constant term to add, we take half of the coefficient of the x term, square it, and add it to both sides of the equation.

So, the coefficient of the x term is -15, half of that is -7.5, and when squared, we get 56.25. We add 56.25 to both sides of the equation:

x^2 - 15x - 10 + 56.25 = 56.25

Now, we can rewrite the left side of the equation as a perfect square trinomial:

(x - 7.5)^2 = 56.25

To solve the equation, we take the square root of both sides:

x - 7.5 = ±√(56.25)

x - 7.5 = ±7.5

Finally, we solve for x by adding 7.5 to both sides:

x = 7.5 ± 7.5

So, the numbers that need to be added to complete the square are ±7.5.