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Simplifying 5p2 + 10p + -30 = 0 Reorder the terms: -30 + 10p + 5p2 = 0 Solving -30 + 10p + 5p2 = 0 Solving for variable 'p'. Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + 2p + p2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + 2p + p2)' equal to zero and attempt to solve: Simplifying -6 + 2p + p2 = 0 Solving -6 + 2p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2p + 6 + p2 = 0 + 6 Reorder the terms: -6 + 6 + 2p + p2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2p + p2 = 0 + 6 2p + p2 = 0 + 6 Combine like terms: 0 + 6 = 6 2p + p2 = 6 The p term is 2p. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2p + 1 + p2 = 6 + 1 Reorder the terms: 1 + 2p + p2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + 2p + p2 = 7 Factor a perfect square on the left side: (p + 1)(p + 1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (p + 1) equal to 2.645751311 and -2.645751311.Subproblem 1
p + 1 = 2.645751311 Simplifying p + 1 = 2.645751311 Reorder the terms: 1 + p = 2.645751311 Solving 1 + p = 2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + p = 2.645751311 + -1 p = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 p = 1.645751311 Simplifying p = 1.645751311Subproblem 2
p + 1 = -2.645751311 Simplifying p + 1 = -2.645751311 Reorder the terms: 1 + p = -2.645751311 Solving 1 + p = -2.645751311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + p = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + p = -2.645751311 + -1 p = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 p = -3.645751311 Simplifying p = -3.645751311Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.645751311, -3.645751311}Solution
p = {1.645751311, -3.645751311}
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