Question

What number needs to be added to both sides of the equation to complete the square?

x2−7x=5



Enter your answers in the boxes.

x2−7x +___= 5 +____

Answer 1

x2−7x + 12.25 = 5 + 12.25

Explanation:

To complete the square for the equation x^2 - 7x = 5, you want to add a specific number to both sides of the equation so that the left side becomes a perfect square trinomial.

First, you need to consider the coefficient of the x-term, which is -7. To complete the square, you add half of this coefficient squared (in this case, (-7/2)^2). This ensures that the quadratic expression on the left side is a perfect square trinomial.

So, you add (-(7/2))^2 to both sides of the equation:

x^2 - 7x + (7/2)^2 = 5 + (7/2)^2

x^2 - 7x + 12.25 = 5 + 12.25

Now, the left side is a perfect square trinomial:

(x - 3.5)^2 = 17.25

So, the equation in the completed square form is:

(x - 3.5)^2 = 17.25

Now you can solve for x.