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Simplifying 4p(p + -2) = 100 Reorder the terms: 4p(-2 + p) = 100 (-2 * 4p + p * 4p) = 100 (-8p + 4p2) = 100 Solving -8p + 4p2 = 100 Solving for variable 'p'. Reorder the terms: -100 + -8p + 4p2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -8p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -2p + p2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -2p + p2)' equal to zero and attempt to solve: Simplifying -25 + -2p + p2 = 0 Solving -25 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -2p + 25 + p2 = 0 + 25 Reorder the terms: -25 + 25 + -2p + p2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -2p + p2 = 0 + 25 -2p + p2 = 0 + 25 Combine like terms: 0 + 25 = 25 -2p + p2 = 25 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 25 + 1 Reorder the terms: 1 + -2p + p2 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + -2p + p2 = 26 Factor a perfect square on the left side: (p + -1)(p + -1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (p + -1) equal to 5.099019514 and -5.099019514.Subproblem 1
p + -1 = 5.099019514 Simplifying p + -1 = 5.099019514 Reorder the terms: -1 + p = 5.099019514 Solving -1 + p = 5.099019514 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + p = 5.099019514 + 1 p = 5.099019514 + 1 Combine like terms: 5.099019514 + 1 = 6.099019514 p = 6.099019514 Simplifying p = 6.099019514Subproblem 2
p + -1 = -5.099019514 Simplifying p + -1 = -5.099019514 Reorder the terms: -1 + p = -5.099019514 Solving -1 + p = -5.099019514 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -5.099019514 + 1 Combine like terms: -1 + 1 = 0 0 + p = -5.099019514 + 1 p = -5.099019514 + 1 Combine like terms: -5.099019514 + 1 = -4.099019514 p = -4.099019514 Simplifying p = -4.099019514Solution
The solution to the problem is based on the solutions from the subproblems. p = {6.099019514, -4.099019514}Solution
p = {6.099019514, -4.099019514}
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