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Simplifying -3p2(5p2 + p + -7) = 0 Reorder the terms: -3p2(-7 + p + 5p2) = 0 (-7 * -3p2 + p * -3p2 + 5p2 * -3p2) = 0 (21p2 + -3p3 + -15p4) = 0 Solving 21p2 + -3p3 + -15p4 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '3p2'. 3p2(7 + -1p + -5p2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve: Simplifying p2 = 0 Solving p2 = 0 Move all terms containing p to the left, all other terms to the right. Simplifying p2 = 0 Take the square root of each side: p = {0}Subproblem 2
Set the factor '(7 + -1p + -5p2)' equal to zero and attempt to solve: Simplifying 7 + -1p + -5p2 = 0 Solving 7 + -1p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.4 + 0.2p + p2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 0.2p + 1.4 + p2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 0.2p + p2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 0.2p + p2 = 0 + 1.4 0.2p + p2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 0.2p + p2 = 1.4 The p term is 0.2p. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2p + 0.01 + p2 = 1.4 + 0.01 Reorder the terms: 0.01 + 0.2p + p2 = 1.4 + 0.01 Combine like terms: 1.4 + 0.01 = 1.41 0.01 + 0.2p + p2 = 1.41 Factor a perfect square on the left side: (p + 0.1)(p + 0.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (p + 0.1) equal to 1.187434209 and -1.187434209.Subproblem 1
p + 0.1 = 1.187434209 Simplifying p + 0.1 = 1.187434209 Reorder the terms: 0.1 + p = 1.187434209 Solving 0.1 + p = 1.187434209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + p = 1.187434209 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + p = 1.187434209 + -0.1 p = 1.187434209 + -0.1 Combine like terms: 1.187434209 + -0.1 = 1.087434209 p = 1.087434209 Simplifying p = 1.087434209Subproblem 2
p + 0.1 = -1.187434209 Simplifying p + 0.1 = -1.187434209 Reorder the terms: 0.1 + p = -1.187434209 Solving 0.1 + p = -1.187434209 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + p = -1.187434209 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + p = -1.187434209 + -0.1 p = -1.187434209 + -0.1 Combine like terms: -1.187434209 + -0.1 = -1.287434209 p = -1.287434209 Simplifying p = -1.287434209Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.087434209, -1.287434209}Solution
p = {0, 1.087434209, -1.287434209}
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