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Simplifying 35p3 + -25p + 15p2 = 0 Reorder the terms: -25p + 15p2 + 35p3 = 0 Solving -25p + 15p2 + 35p3 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5p'. 5p(-5 + 3p + 7p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'p' equal to zero and attempt to solve: Simplifying p = 0 Solving p = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p = 0Subproblem 2
Set the factor '(-5 + 3p + 7p2)' equal to zero and attempt to solve: Simplifying -5 + 3p + 7p2 = 0 Solving -5 + 3p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.7142857143 + 0.4285714286p + p2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + 0.4285714286p + 0.7142857143 + p2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + 0.4285714286p + p2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + 0.4285714286p + p2 = 0 + 0.7142857143 0.4285714286p + p2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 0.4285714286p + p2 = 0.7142857143 The p term is 0.4285714286p. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286p + 0.04591836735 + p2 = 0.7142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286p + p2 = 0.7142857143 + 0.04591836735 Combine like terms: 0.7142857143 + 0.04591836735 = 0.76020408165 0.04591836735 + 0.4285714286p + p2 = 0.76020408165 Factor a perfect square on the left side: (p + 0.2142857143)(p + 0.2142857143) = 0.76020408165 Calculate the square root of the right side: 0.87189683 Break this problem into two subproblems by setting (p + 0.2142857143) equal to 0.87189683 and -0.87189683.Subproblem 1
p + 0.2142857143 = 0.87189683 Simplifying p + 0.2142857143 = 0.87189683 Reorder the terms: 0.2142857143 + p = 0.87189683 Solving 0.2142857143 + p = 0.87189683 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + p = 0.87189683 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + p = 0.87189683 + -0.2142857143 p = 0.87189683 + -0.2142857143 Combine like terms: 0.87189683 + -0.2142857143 = 0.6576111157 p = 0.6576111157 Simplifying p = 0.6576111157Subproblem 2
p + 0.2142857143 = -0.87189683 Simplifying p + 0.2142857143 = -0.87189683 Reorder the terms: 0.2142857143 + p = -0.87189683 Solving 0.2142857143 + p = -0.87189683 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + p = -0.87189683 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + p = -0.87189683 + -0.2142857143 p = -0.87189683 + -0.2142857143 Combine like terms: -0.87189683 + -0.2142857143 = -1.0861825443 p = -1.0861825443 Simplifying p = -1.0861825443Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.6576111157, -1.0861825443}Solution
p = {0, 0.6576111157, -1.0861825443}
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