Question

2
Rewrite the equation in the form (x-p)² = q.
0=x²-10x + 13

Answer 1

To rewrite the quadratic equation 0 = x² - 10x + 13 in the form (x - p)² = q, we complete the square by adding 25 to both sides, resulting in (x - 5)² = 12 with p = 5 and q = 12.

Step-by-step explanation:

To rewrite the equation 0 = x² - 10x + 13 in the form (x - p)² = q, we need to complete the square. First, we transfer the constant term to the other side:

x²-10x = -13

Now, we find the value that needs to be added to both sides to complete the square. We take half the coefficient of x, which is -10/2 = -5, and square it, resulting in 25. We add this value to both sides:

x² - 10x + 25 = -13 + 25

This gives us:

(x - 5)² = 12

Now the equation is in the desired form, with p = 5 and q = 12.