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Simplifying 5p2 + -7p = 4 + -9p Reorder the terms: -7p + 5p2 = 4 + -9p Solving -7p + 5p2 = 4 + -9p Solving for variable 'p'. Reorder the terms: -4 + -7p + 9p + 5p2 = 4 + -9p + -4 + 9p Combine like terms: -7p + 9p = 2p -4 + 2p + 5p2 = 4 + -9p + -4 + 9p Reorder the terms: -4 + 2p + 5p2 = 4 + -4 + -9p + 9p Combine like terms: 4 + -4 = 0 -4 + 2p + 5p2 = 0 + -9p + 9p -4 + 2p + 5p2 = -9p + 9p Combine like terms: -9p + 9p = 0 -4 + 2p + 5p2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.4p + p2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.4p + 0.8 + p2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.4p + p2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.4p + p2 = 0 + 0.8 0.4p + p2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.4p + p2 = 0.8 The p term is 0.4p. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4p + 0.04 + p2 = 0.8 + 0.04 Reorder the terms: 0.04 + 0.4p + p2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + 0.4p + p2 = 0.84 Factor a perfect square on the left side: (p + 0.2)(p + 0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (p + 0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
p + 0.2 = 0.916515139 Simplifying p + 0.2 = 0.916515139 Reorder the terms: 0.2 + p = 0.916515139 Solving 0.2 + p = 0.916515139 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + p = 0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + p = 0.916515139 + -0.2 p = 0.916515139 + -0.2 Combine like terms: 0.916515139 + -0.2 = 0.716515139 p = 0.716515139 Simplifying p = 0.716515139Subproblem 2
p + 0.2 = -0.916515139 Simplifying p + 0.2 = -0.916515139 Reorder the terms: 0.2 + p = -0.916515139 Solving 0.2 + p = -0.916515139 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + p = -0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + p = -0.916515139 + -0.2 p = -0.916515139 + -0.2 Combine like terms: -0.916515139 + -0.2 = -1.116515139 p = -1.116515139 Simplifying p = -1.116515139Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.716515139, -1.116515139}
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