Question

Consider the equation: -34=x^2-14x-10. 1) Rewrite the equation by completing the square. Your equation should look like (x-a)^2=b or (x-c)^2=d.

Answer 1

The completed square form of the equation -34 = x^2 - 14x - 10 is (x - 7)^2 = 93, accomplished by isolating the quadratic and linear terms and adding the square of half the coefficient of x to both sides.

Step-by-step explanation:

To rewrite the equation -34 = x^2 - 14x - 10 by completing the square, first, we need to isolate the quadratic and linear terms on one side of the equation. Let's move -34 to the right side.

x^2 - 14x = 44

Now, to complete the square, we must add a term that creates a perfect square trinomial on the left side of the equation. This term will be the square of half of the coefficient of x, which is (-14/2)^2 = 49.

Add 49 to both sides:

x^2 - 14x + 49 = 44 + 49

Now we have a perfect square trinomial on the left side:

(x - 7)^2 = 93

Thus, the completed square form of the equation is (x - 7)^2 = 93.