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Simplifying 6p2 + 10p + -36 = 0 Reorder the terms: -36 + 10p + 6p2 = 0 Solving -36 + 10p + 6p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 5p + 3p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-18 + 5p + 3p2)' equal to zero and attempt to solve: Simplifying -18 + 5p + 3p2 = 0 Solving -18 + 5p + 3p2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6 + 1.666666667p + p2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.666666667p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + 1.666666667p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.666666667p + p2 = 0 + 6 1.666666667p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.666666667p + p2 = 6 The p term is 1.666666667p. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667p + 0.6944444447 + p2 = 6 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667p + p2 = 6 + 0.6944444447 Combine like terms: 6 + 0.6944444447 = 6.6944444447 0.6944444447 + 1.666666667p + p2 = 6.6944444447 Factor a perfect square on the left side: (p + 0.8333333335)(p + 0.8333333335) = 6.6944444447 Calculate the square root of the right side: 2.587362449 Break this problem into two subproblems by setting (p + 0.8333333335) equal to 2.587362449 and -2.587362449.Subproblem 1
p + 0.8333333335 = 2.587362449 Simplifying p + 0.8333333335 = 2.587362449 Reorder the terms: 0.8333333335 + p = 2.587362449 Solving 0.8333333335 + p = 2.587362449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + p = 2.587362449 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + p = 2.587362449 + -0.8333333335 p = 2.587362449 + -0.8333333335 Combine like terms: 2.587362449 + -0.8333333335 = 1.7540291155 p = 1.7540291155 Simplifying p = 1.7540291155Subproblem 2
p + 0.8333333335 = -2.587362449 Simplifying p + 0.8333333335 = -2.587362449 Reorder the terms: 0.8333333335 + p = -2.587362449 Solving 0.8333333335 + p = -2.587362449 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + p = -2.587362449 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + p = -2.587362449 + -0.8333333335 p = -2.587362449 + -0.8333333335 Combine like terms: -2.587362449 + -0.8333333335 = -3.4206957825 p = -3.4206957825 Simplifying p = -3.4206957825Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.7540291155, -3.4206957825}Solution
p = {1.7540291155, -3.4206957825}
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