The values of p and q are p = 3/2 and q = 9
To solve this problem
Extend the equation's right side as follows:
4x² + 12x = 4(x² + 2px + p²) - q
Combine like terms:
4x² + 12x = 4x² + 8px + 4p² - q
Equate the coefficients of each term on both sides:
• x coefficient: 12 = 8p
• Constant term: -q = 4p²
Solve for p:
• From the x coefficient equation: p = 12/8 = 3/2
Substitute p = 3/2 into the constant term equation:
-q = 4(3/2)²
-q = 4 * 9/4
-q = 9
Solve for q:
q = 9
Therefore, the values of p and q are p = 3/2 and q = 9