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Simplifying 5p2 = 30p + 40 Reorder the terms: 5p2 = 40 + 30p Solving 5p2 = 40 + 30p Solving for variable 'p'. Reorder the terms: -40 + -30p + 5p2 = 40 + 30p + -40 + -30p Reorder the terms: -40 + -30p + 5p2 = 40 + -40 + 30p + -30p Combine like terms: 40 + -40 = 0 -40 + -30p + 5p2 = 0 + 30p + -30p -40 + -30p + 5p2 = 30p + -30p Combine like terms: 30p + -30p = 0 -40 + -30p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + -6p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + -6p + p2)' equal to zero and attempt to solve: Simplifying -8 + -6p + p2 = 0 Solving -8 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6p + 8 + p2 = 0 + 8 Reorder the terms: -8 + 8 + -6p + p2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6p + p2 = 0 + 8 -6p + p2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6p + p2 = 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 = 8 + 9 Reorder the terms: 9 + -6p + p2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6p + p2 = 17 Factor a perfect square on the left side: (p + -3)(p + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (p + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
p + -3 = 4.123105626 Simplifying p + -3 = 4.123105626 Reorder the terms: -3 + p = 4.123105626 Solving -3 + p = 4.123105626 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 = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + p = 4.123105626 + 3 p = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 p = 7.123105626 Simplifying p = 7.123105626Subproblem 2
p + -3 = -4.123105626 Simplifying p + -3 = -4.123105626 Reorder the terms: -3 + p = -4.123105626 Solving -3 + p = -4.123105626 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 = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + p = -4.123105626 + 3 p = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 p = -1.123105626 Simplifying p = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. p = {7.123105626, -1.123105626}Solution
p = {7.123105626, -1.123105626}
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