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Simplifying 14p2 + 26p + -100 = 0 Reorder the terms: -100 + 26p + 14p2 = 0 Solving -100 + 26p + 14p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 13p + 7p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 13p + 7p2)' equal to zero and attempt to solve: Simplifying -50 + 13p + 7p2 = 0 Solving -50 + 13p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7.142857143 + 1.857142857p + p2 = 0 Move the constant term to the right: Add '7.142857143' to each side of the equation. -7.142857143 + 1.857142857p + 7.142857143 + p2 = 0 + 7.142857143 Reorder the terms: -7.142857143 + 7.142857143 + 1.857142857p + p2 = 0 + 7.142857143 Combine like terms: -7.142857143 + 7.142857143 = 0.000000000 0.000000000 + 1.857142857p + p2 = 0 + 7.142857143 1.857142857p + p2 = 0 + 7.142857143 Combine like terms: 0 + 7.142857143 = 7.142857143 1.857142857p + p2 = 7.142857143 The p term is 1.857142857p. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857p + 0.8622448978 + p2 = 7.142857143 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857p + p2 = 7.142857143 + 0.8622448978 Combine like terms: 7.142857143 + 0.8622448978 = 8.0051020408 0.8622448978 + 1.857142857p + p2 = 8.0051020408 Factor a perfect square on the left side: (p + 0.9285714285)(p + 0.9285714285) = 8.0051020408 Calculate the square root of the right side: 2.829328903 Break this problem into two subproblems by setting (p + 0.9285714285) equal to 2.829328903 and -2.829328903.Subproblem 1
p + 0.9285714285 = 2.829328903 Simplifying p + 0.9285714285 = 2.829328903 Reorder the terms: 0.9285714285 + p = 2.829328903 Solving 0.9285714285 + p = 2.829328903 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + p = 2.829328903 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + p = 2.829328903 + -0.9285714285 p = 2.829328903 + -0.9285714285 Combine like terms: 2.829328903 + -0.9285714285 = 1.9007574745 p = 1.9007574745 Simplifying p = 1.9007574745Subproblem 2
p + 0.9285714285 = -2.829328903 Simplifying p + 0.9285714285 = -2.829328903 Reorder the terms: 0.9285714285 + p = -2.829328903 Solving 0.9285714285 + p = -2.829328903 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + p = -2.829328903 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + p = -2.829328903 + -0.9285714285 p = -2.829328903 + -0.9285714285 Combine like terms: -2.829328903 + -0.9285714285 = -3.7579003315 p = -3.7579003315 Simplifying p = -3.7579003315Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.9007574745, -3.7579003315}Solution
p = {1.9007574745, -3.7579003315}
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