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Simplifying 4p2 = 20 + -10p Solving 4p2 = 20 + -10p Solving for variable 'p'. Reorder the terms: -20 + 10p + 4p2 = 20 + -10p + -20 + 10p Reorder the terms: -20 + 10p + 4p2 = 20 + -20 + -10p + 10p Combine like terms: 20 + -20 = 0 -20 + 10p + 4p2 = 0 + -10p + 10p -20 + 10p + 4p2 = -10p + 10p Combine like terms: -10p + 10p = 0 -20 + 10p + 4p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 5p + 2p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 5p + 2p2)' equal to zero and attempt to solve: Simplifying -10 + 5p + 2p2 = 0 Solving -10 + 5p + 2p2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 2.5p + p2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.5p + 5 + p2 = 0 + 5 Reorder the terms: -5 + 5 + 2.5p + p2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.5p + p2 = 0 + 5 2.5p + p2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.5p + p2 = 5 The p term is 2.5p. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5p + 1.5625 + p2 = 5 + 1.5625 Reorder the terms: 1.5625 + 2.5p + p2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + 2.5p + p2 = 6.5625 Factor a perfect square on the left side: (p + 1.25)(p + 1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (p + 1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
p + 1.25 = 2.561737691 Simplifying p + 1.25 = 2.561737691 Reorder the terms: 1.25 + p = 2.561737691 Solving 1.25 + p = 2.561737691 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + p = 2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + p = 2.561737691 + -1.25 p = 2.561737691 + -1.25 Combine like terms: 2.561737691 + -1.25 = 1.311737691 p = 1.311737691 Simplifying p = 1.311737691Subproblem 2
p + 1.25 = -2.561737691 Simplifying p + 1.25 = -2.561737691 Reorder the terms: 1.25 + p = -2.561737691 Solving 1.25 + p = -2.561737691 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + p = -2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + p = -2.561737691 + -1.25 p = -2.561737691 + -1.25 Combine like terms: -2.561737691 + -1.25 = -3.811737691 p = -3.811737691 Simplifying p = -3.811737691Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.311737691, -3.811737691}Solution
p = {1.311737691, -3.811737691}
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