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Simplifying (3p + -4)(p + 3) = 15 Reorder the terms: (-4 + 3p)(p + 3) = 15 Reorder the terms: (-4 + 3p)(3 + p) = 15 Multiply (-4 + 3p) * (3 + p) (-4(3 + p) + 3p * (3 + p)) = 15 ((3 * -4 + p * -4) + 3p * (3 + p)) = 15 ((-12 + -4p) + 3p * (3 + p)) = 15 (-12 + -4p + (3 * 3p + p * 3p)) = 15 (-12 + -4p + (9p + 3p2)) = 15 Combine like terms: -4p + 9p = 5p (-12 + 5p + 3p2) = 15 Solving -12 + 5p + 3p2 = 15 Solving for variable 'p'. Reorder the terms: -12 + -15 + 5p + 3p2 = 15 + -15 Combine like terms: -12 + -15 = -27 -27 + 5p + 3p2 = 15 + -15 Combine like terms: 15 + -15 = 0 -27 + 5p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9 + 1.666666667p + p2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 1.666666667p + 9 + p2 = 0 + 9 Reorder the terms: -9 + 9 + 1.666666667p + p2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 1.666666667p + p2 = 0 + 9 1.666666667p + p2 = 0 + 9 Combine like terms: 0 + 9 = 9 1.666666667p + p2 = 9 The p term is 1.666666667p. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667p + 0.6944444447 + p2 = 9 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667p + p2 = 9 + 0.6944444447 Combine like terms: 9 + 0.6944444447 = 9.6944444447 0.6944444447 + 1.666666667p + p2 = 9.6944444447 Factor a perfect square on the left side: (p + 0.8333333335)(p + 0.8333333335) = 9.6944444447 Calculate the square root of the right side: 3.113590282 Break this problem into two subproblems by setting (p + 0.8333333335) equal to 3.113590282 and -3.113590282.Subproblem 1
p + 0.8333333335 = 3.113590282 Simplifying p + 0.8333333335 = 3.113590282 Reorder the terms: 0.8333333335 + p = 3.113590282 Solving 0.8333333335 + p = 3.113590282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + p = 3.113590282 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + p = 3.113590282 + -0.8333333335 p = 3.113590282 + -0.8333333335 Combine like terms: 3.113590282 + -0.8333333335 = 2.2802569485 p = 2.2802569485 Simplifying p = 2.2802569485Subproblem 2
p + 0.8333333335 = -3.113590282 Simplifying p + 0.8333333335 = -3.113590282 Reorder the terms: 0.8333333335 + p = -3.113590282 Solving 0.8333333335 + p = -3.113590282 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + p = -3.113590282 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + p = -3.113590282 + -0.8333333335 p = -3.113590282 + -0.8333333335 Combine like terms: -3.113590282 + -0.8333333335 = -3.9469236155 p = -3.9469236155 Simplifying p = -3.9469236155Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.2802569485, -3.9469236155}
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