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Simplifying 5p2 + -25 = 4p + 24 Reorder the terms: -25 + 5p2 = 4p + 24 Reorder the terms: -25 + 5p2 = 24 + 4p Solving -25 + 5p2 = 24 + 4p Solving for variable 'p'. Reorder the terms: -25 + -24 + -4p + 5p2 = 24 + 4p + -24 + -4p Combine like terms: -25 + -24 = -49 -49 + -4p + 5p2 = 24 + 4p + -24 + -4p Reorder the terms: -49 + -4p + 5p2 = 24 + -24 + 4p + -4p Combine like terms: 24 + -24 = 0 -49 + -4p + 5p2 = 0 + 4p + -4p -49 + -4p + 5p2 = 4p + -4p Combine like terms: 4p + -4p = 0 -49 + -4p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9.8 + -0.8p + p2 = 0 Move the constant term to the right: Add '9.8' to each side of the equation. -9.8 + -0.8p + 9.8 + p2 = 0 + 9.8 Reorder the terms: -9.8 + 9.8 + -0.8p + p2 = 0 + 9.8 Combine like terms: -9.8 + 9.8 = 0.0 0.0 + -0.8p + p2 = 0 + 9.8 -0.8p + p2 = 0 + 9.8 Combine like terms: 0 + 9.8 = 9.8 -0.8p + p2 = 9.8 The p term is -0.8p. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8p + 0.16 + p2 = 9.8 + 0.16 Reorder the terms: 0.16 + -0.8p + p2 = 9.8 + 0.16 Combine like terms: 9.8 + 0.16 = 9.96 0.16 + -0.8p + p2 = 9.96 Factor a perfect square on the left side: (p + -0.4)(p + -0.4) = 9.96 Calculate the square root of the right side: 3.155946768 Break this problem into two subproblems by setting (p + -0.4) equal to 3.155946768 and -3.155946768.Subproblem 1
p + -0.4 = 3.155946768 Simplifying p + -0.4 = 3.155946768 Reorder the terms: -0.4 + p = 3.155946768 Solving -0.4 + p = 3.155946768 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = 3.155946768 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = 3.155946768 + 0.4 p = 3.155946768 + 0.4 Combine like terms: 3.155946768 + 0.4 = 3.555946768 p = 3.555946768 Simplifying p = 3.555946768Subproblem 2
p + -0.4 = -3.155946768 Simplifying p + -0.4 = -3.155946768 Reorder the terms: -0.4 + p = -3.155946768 Solving -0.4 + p = -3.155946768 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + p = -3.155946768 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + p = -3.155946768 + 0.4 p = -3.155946768 + 0.4 Combine like terms: -3.155946768 + 0.4 = -2.755946768 p = -2.755946768 Simplifying p = -2.755946768Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.555946768, -2.755946768}
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