Question

The equation 2x² -5x = -12 is rewritten in the form of

2(x-p)² +q=0. What is the value of p?
(round to the nearest hundredth)

Answer 1

To rewrite the equation 2x² -5x = -12 in the form of 2(x-p)² +q=0, we complete the square and find that p is equal to 5/4.

Step-by-step explanation:

To rewrite the equation 2x² -5x = -12 in the form of 2(x-p)² +q=0, we need to complete the square. First, let's divide both sides of the equation by 2:

x² - (5/2)x = -6

To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² - (5/2)x + (-5/4)² = -6 + (-5/4)²

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

x² - (5/2)x + (-5/4)² = (x - (5/4))² = -6 + (-5/4)²

Comparing this with the given form 2(x-p)² + q = 0, we can see that p is equal to 5/4.

Learn more about Rewriting equations in the form of (x-p)²