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Simplifying 5p2 + -9p + -10 = 0 Reorder the terms: -10 + -9p + 5p2 = 0 Solving -10 + -9p + 5p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -1.8p + p2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.8p + 2 + p2 = 0 + 2 Reorder the terms: -2 + 2 + -1.8p + p2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.8p + p2 = 0 + 2 -1.8p + p2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.8p + p2 = 2 The p term is -1.8p. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8p + 0.81 + p2 = 2 + 0.81 Reorder the terms: 0.81 + -1.8p + p2 = 2 + 0.81 Combine like terms: 2 + 0.81 = 2.81 0.81 + -1.8p + p2 = 2.81 Factor a perfect square on the left side: (p + -0.9)(p + -0.9) = 2.81 Calculate the square root of the right side: 1.676305461 Break this problem into two subproblems by setting (p + -0.9) equal to 1.676305461 and -1.676305461.Subproblem 1
p + -0.9 = 1.676305461 Simplifying p + -0.9 = 1.676305461 Reorder the terms: -0.9 + p = 1.676305461 Solving -0.9 + p = 1.676305461 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + p = 1.676305461 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + p = 1.676305461 + 0.9 p = 1.676305461 + 0.9 Combine like terms: 1.676305461 + 0.9 = 2.576305461 p = 2.576305461 Simplifying p = 2.576305461Subproblem 2
p + -0.9 = -1.676305461 Simplifying p + -0.9 = -1.676305461 Reorder the terms: -0.9 + p = -1.676305461 Solving -0.9 + p = -1.676305461 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + p = -1.676305461 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + p = -1.676305461 + 0.9 p = -1.676305461 + 0.9 Combine like terms: -1.676305461 + 0.9 = -0.776305461 p = -0.776305461 Simplifying p = -0.776305461Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.576305461, -0.776305461}
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