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Simplifying 5p2 + -25p = 4p2 + 24 Reorder the terms: -25p + 5p2 = 4p2 + 24 Reorder the terms: -25p + 5p2 = 24 + 4p2 Solving -25p + 5p2 = 24 + 4p2 Solving for variable 'p'. Reorder the terms: -24 + -25p + 5p2 + -4p2 = 24 + 4p2 + -24 + -4p2 Combine like terms: 5p2 + -4p2 = 1p2 -24 + -25p + 1p2 = 24 + 4p2 + -24 + -4p2 Reorder the terms: -24 + -25p + 1p2 = 24 + -24 + 4p2 + -4p2 Combine like terms: 24 + -24 = 0 -24 + -25p + 1p2 = 0 + 4p2 + -4p2 -24 + -25p + 1p2 = 4p2 + -4p2 Combine like terms: 4p2 + -4p2 = 0 -24 + -25p + 1p2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -25p + 24 + p2 = 0 + 24 Reorder the terms: -24 + 24 + -25p + p2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -25p + p2 = 0 + 24 -25p + p2 = 0 + 24 Combine like terms: 0 + 24 = 24 -25p + p2 = 24 The p term is -25p. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25p + 156.25 + p2 = 24 + 156.25 Reorder the terms: 156.25 + -25p + p2 = 24 + 156.25 Combine like terms: 24 + 156.25 = 180.25 156.25 + -25p + p2 = 180.25 Factor a perfect square on the left side: (p + -12.5)(p + -12.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (p + -12.5) equal to 13.425721582 and -13.425721582.Subproblem 1
p + -12.5 = 13.425721582 Simplifying p + -12.5 = 13.425721582 Reorder the terms: -12.5 + p = 13.425721582 Solving -12.5 + p = 13.425721582 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + p = 13.425721582 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + p = 13.425721582 + 12.5 p = 13.425721582 + 12.5 Combine like terms: 13.425721582 + 12.5 = 25.925721582 p = 25.925721582 Simplifying p = 25.925721582Subproblem 2
p + -12.5 = -13.425721582 Simplifying p + -12.5 = -13.425721582 Reorder the terms: -12.5 + p = -13.425721582 Solving -12.5 + p = -13.425721582 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + p = -13.425721582 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + p = -13.425721582 + 12.5 p = -13.425721582 + 12.5 Combine like terms: -13.425721582 + 12.5 = -0.925721582 p = -0.925721582 Simplifying p = -0.925721582Solution
The solution to the problem is based on the solutions from the subproblems. p = {25.925721582, -0.925721582}
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