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Simplifying 3p2 + -18p = 141 Reorder the terms: -18p + 3p2 = 141 Solving -18p + 3p2 = 141 Solving for variable 'p'. Reorder the terms: -141 + -18p + 3p2 = 141 + -141 Combine like terms: 141 + -141 = 0 -141 + -18p + 3p2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-47 + -6p + p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-47 + -6p + p2)' equal to zero and attempt to solve: Simplifying -47 + -6p + p2 = 0 Solving -47 + -6p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -6p + 47 + p2 = 0 + 47 Reorder the terms: -47 + 47 + -6p + p2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -6p + p2 = 0 + 47 -6p + p2 = 0 + 47 Combine like terms: 0 + 47 = 47 -6p + p2 = 47 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 = 47 + 9 Reorder the terms: 9 + -6p + p2 = 47 + 9 Combine like terms: 47 + 9 = 56 9 + -6p + p2 = 56 Factor a perfect square on the left side: (p + -3)(p + -3) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (p + -3) equal to 7.483314774 and -7.483314774.Subproblem 1
p + -3 = 7.483314774 Simplifying p + -3 = 7.483314774 Reorder the terms: -3 + p = 7.483314774 Solving -3 + p = 7.483314774 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 = 7.483314774 + 3 Combine like terms: -3 + 3 = 0 0 + p = 7.483314774 + 3 p = 7.483314774 + 3 Combine like terms: 7.483314774 + 3 = 10.483314774 p = 10.483314774 Simplifying p = 10.483314774Subproblem 2
p + -3 = -7.483314774 Simplifying p + -3 = -7.483314774 Reorder the terms: -3 + p = -7.483314774 Solving -3 + p = -7.483314774 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 = -7.483314774 + 3 Combine like terms: -3 + 3 = 0 0 + p = -7.483314774 + 3 p = -7.483314774 + 3 Combine like terms: -7.483314774 + 3 = -4.483314774 p = -4.483314774 Simplifying p = -4.483314774Solution
The solution to the problem is based on the solutions from the subproblems. p = {10.483314774, -4.483314774}Solution
p = {10.483314774, -4.483314774}
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