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Simplifying -4p2 + -10p + -55 = -9p2 Reorder the terms: -55 + -10p + -4p2 = -9p2 Solving -55 + -10p + -4p2 = -9p2 Solving for variable 'p'. Combine like terms: -4p2 + 9p2 = 5p2 -55 + -10p + 5p2 = -9p2 + 9p2 Combine like terms: -9p2 + 9p2 = 0 -55 + -10p + 5p2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-11 + -2p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-11 + -2p + p2)' equal to zero and attempt to solve: Simplifying -11 + -2p + p2 = 0 Solving -11 + -2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -2p + 11 + p2 = 0 + 11 Reorder the terms: -11 + 11 + -2p + p2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2p + p2 = 0 + 11 -2p + p2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2p + p2 = 11 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 = 11 + 1 Reorder the terms: 1 + -2p + p2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2p + p2 = 12 Factor a perfect square on the left side: (p + -1)(p + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (p + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
p + -1 = 3.464101615 Simplifying p + -1 = 3.464101615 Reorder the terms: -1 + p = 3.464101615 Solving -1 + p = 3.464101615 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 = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + p = 3.464101615 + 1 p = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 p = 4.464101615 Simplifying p = 4.464101615Subproblem 2
p + -1 = -3.464101615 Simplifying p + -1 = -3.464101615 Reorder the terms: -1 + p = -3.464101615 Solving -1 + p = -3.464101615 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 = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + p = -3.464101615 + 1 p = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 p = -2.464101615 Simplifying p = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.464101615, -2.464101615}Solution
p = {4.464101615, -2.464101615}
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