Question

If the quadratic equation 22x² +5= -6x is written in the form(x– p)² = q. What is the value of p?

Hint: Complete the Square.
A) p=-3/2
B) p=-5/2
C) p=5/2
D) p=3/2

Answer 1

To write the quadratic equation 22x² +5= -6x in the form (x– p)² = q, we need to complete the square. The value of p is p = -3/22.

Step-by-step explanation:

To write the quadratic equation 22x² +5= -6x in the form (x– p)² = q, we need to complete the square. Here's how:

Step 1: Move all the terms to one side of the equation to get 22x² + 6x + 5 = 0.

Step 2: Divide the entire equation by the coefficient of x², which is 22, to get x² + (6/22)x + (5/22) = 0.

Step 3: Complete the square by adding the square of half the coefficient of x to both sides of the equation. Half of 6/22 is 3/22, so we add (3/22)² to both sides to get x² + (6/22)x + (3/22)² + (5/22) - (3/22)² = 0.

Step 4: Simplify the equation to get (x + 3/22)² = 5/22 - 9/484.

Step 5: Rewrite the equation in the form (x – p)² = q by letting p = -3/22 and q = 5/22 - 9/484. Therefore, the value of p is p = -3/22.