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Simplifying 21 = 2p2 + -5p Reorder the terms: 21 = -5p + 2p2 Solving 21 = -5p + 2p2 Solving for variable 'p'. Reorder the terms: 21 + 5p + -2p2 = -5p + 5p + 2p2 + -2p2 Combine like terms: -5p + 5p = 0 21 + 5p + -2p2 = 0 + 2p2 + -2p2 21 + 5p + -2p2 = 2p2 + -2p2 Combine like terms: 2p2 + -2p2 = 0 21 + 5p + -2p2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -10.5 + -2.5p + p2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + -2.5p + 10.5 + p2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + -2.5p + p2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + -2.5p + p2 = 0 + 10.5 -2.5p + p2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 -2.5p + p2 = 10.5 The p term is -2.5p. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5p + 1.5625 + p2 = 10.5 + 1.5625 Reorder the terms: 1.5625 + -2.5p + p2 = 10.5 + 1.5625 Combine like terms: 10.5 + 1.5625 = 12.0625 1.5625 + -2.5p + p2 = 12.0625 Factor a perfect square on the left side: (p + -1.25)(p + -1.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (p + -1.25) equal to 3.473110997 and -3.473110997.Subproblem 1
p + -1.25 = 3.473110997 Simplifying p + -1.25 = 3.473110997 Reorder the terms: -1.25 + p = 3.473110997 Solving -1.25 + p = 3.473110997 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = 3.473110997 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = 3.473110997 + 1.25 p = 3.473110997 + 1.25 Combine like terms: 3.473110997 + 1.25 = 4.723110997 p = 4.723110997 Simplifying p = 4.723110997Subproblem 2
p + -1.25 = -3.473110997 Simplifying p + -1.25 = -3.473110997 Reorder the terms: -1.25 + p = -3.473110997 Solving -1.25 + p = -3.473110997 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + p = -3.473110997 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + p = -3.473110997 + 1.25 p = -3.473110997 + 1.25 Combine like terms: -3.473110997 + 1.25 = -2.223110997 p = -2.223110997 Simplifying p = -2.223110997Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.723110997, -2.223110997}
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