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Simplifying 42p2 + -124p = 32 Reorder the terms: -124p + 42p2 = 32 Solving -124p + 42p2 = 32 Solving for variable 'p'. Reorder the terms: -32 + -124p + 42p2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -124p + 42p2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -62p + 21p2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -62p + 21p2)' equal to zero and attempt to solve: Simplifying -16 + -62p + 21p2 = 0 Solving -16 + -62p + 21p2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.7619047619 + -2.952380952p + p2 = 0 Move the constant term to the right: Add '0.7619047619' to each side of the equation. -0.7619047619 + -2.952380952p + 0.7619047619 + p2 = 0 + 0.7619047619 Reorder the terms: -0.7619047619 + 0.7619047619 + -2.952380952p + p2 = 0 + 0.7619047619 Combine like terms: -0.7619047619 + 0.7619047619 = 0.0000000000 0.0000000000 + -2.952380952p + p2 = 0 + 0.7619047619 -2.952380952p + p2 = 0 + 0.7619047619 Combine like terms: 0 + 0.7619047619 = 0.7619047619 -2.952380952p + p2 = 0.7619047619 The p term is -2.952380952p. Take half its coefficient (-1.476190476). Square it (2.179138321) and add it to both sides. Add '2.179138321' to each side of the equation. -2.952380952p + 2.179138321 + p2 = 0.7619047619 + 2.179138321 Reorder the terms: 2.179138321 + -2.952380952p + p2 = 0.7619047619 + 2.179138321 Combine like terms: 0.7619047619 + 2.179138321 = 2.9410430829 2.179138321 + -2.952380952p + p2 = 2.9410430829 Factor a perfect square on the left side: (p + -1.476190476)(p + -1.476190476) = 2.9410430829 Calculate the square root of the right side: 1.714946962 Break this problem into two subproblems by setting (p + -1.476190476) equal to 1.714946962 and -1.714946962.Subproblem 1
p + -1.476190476 = 1.714946962 Simplifying p + -1.476190476 = 1.714946962 Reorder the terms: -1.476190476 + p = 1.714946962 Solving -1.476190476 + p = 1.714946962 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.476190476' to each side of the equation. -1.476190476 + 1.476190476 + p = 1.714946962 + 1.476190476 Combine like terms: -1.476190476 + 1.476190476 = 0.000000000 0.000000000 + p = 1.714946962 + 1.476190476 p = 1.714946962 + 1.476190476 Combine like terms: 1.714946962 + 1.476190476 = 3.191137438 p = 3.191137438 Simplifying p = 3.191137438Subproblem 2
p + -1.476190476 = -1.714946962 Simplifying p + -1.476190476 = -1.714946962 Reorder the terms: -1.476190476 + p = -1.714946962 Solving -1.476190476 + p = -1.714946962 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.476190476' to each side of the equation. -1.476190476 + 1.476190476 + p = -1.714946962 + 1.476190476 Combine like terms: -1.476190476 + 1.476190476 = 0.000000000 0.000000000 + p = -1.714946962 + 1.476190476 p = -1.714946962 + 1.476190476 Combine like terms: -1.714946962 + 1.476190476 = -0.238756486 p = -0.238756486 Simplifying p = -0.238756486Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.191137438, -0.238756486}Solution
p = {3.191137438, -0.238756486}
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