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Simplifying -5p2 + -30p = 29 Reorder the terms: -30p + -5p2 = 29 Solving -30p + -5p2 = 29 Solving for variable 'p'. Reorder the terms: -29 + -30p + -5p2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + -30p + -5p2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(29 + 30p + 5p2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(29 + 30p + 5p2)' equal to zero and attempt to solve: Simplifying 29 + 30p + 5p2 = 0 Solving 29 + 30p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.8 + 6p + p2 = 0 Move the constant term to the right: Add '-5.8' to each side of the equation. 5.8 + 6p + -5.8 + p2 = 0 + -5.8 Reorder the terms: 5.8 + -5.8 + 6p + p2 = 0 + -5.8 Combine like terms: 5.8 + -5.8 = 0.0 0.0 + 6p + p2 = 0 + -5.8 6p + p2 = 0 + -5.8 Combine like terms: 0 + -5.8 = -5.8 6p + p2 = -5.8 The p term is 6p. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6p + 9 + p2 = -5.8 + 9 Reorder the terms: 9 + 6p + p2 = -5.8 + 9 Combine like terms: -5.8 + 9 = 3.2 9 + 6p + p2 = 3.2 Factor a perfect square on the left side: (p + 3)(p + 3) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (p + 3) equal to 1.788854382 and -1.788854382.Subproblem 1
p + 3 = 1.788854382 Simplifying p + 3 = 1.788854382 Reorder the terms: 3 + p = 1.788854382 Solving 3 + p = 1.788854382 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 1.788854382 + -3 Combine like terms: 3 + -3 = 0 0 + p = 1.788854382 + -3 p = 1.788854382 + -3 Combine like terms: 1.788854382 + -3 = -1.211145618 p = -1.211145618 Simplifying p = -1.211145618Subproblem 2
p + 3 = -1.788854382 Simplifying p + 3 = -1.788854382 Reorder the terms: 3 + p = -1.788854382 Solving 3 + p = -1.788854382 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -1.788854382 + -3 Combine like terms: 3 + -3 = 0 0 + p = -1.788854382 + -3 p = -1.788854382 + -3 Combine like terms: -1.788854382 + -3 = -4.788854382 p = -4.788854382 Simplifying p = -4.788854382Solution
The solution to the problem is based on the solutions from the subproblems. p = {-1.211145618, -4.788854382}Solution
p = {-1.211145618, -4.788854382}
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