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Simplifying 11p2 = 8 + -10p Solving 11p2 = 8 + -10p Solving for variable 'p'. Reorder the terms: -8 + 10p + 11p2 = 8 + -10p + -8 + 10p Reorder the terms: -8 + 10p + 11p2 = 8 + -8 + -10p + 10p Combine like terms: 8 + -8 = 0 -8 + 10p + 11p2 = 0 + -10p + 10p -8 + 10p + 11p2 = -10p + 10p Combine like terms: -10p + 10p = 0 -8 + 10p + 11p2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.7272727273 + 0.9090909091p + p2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + 0.9090909091p + 0.7272727273 + p2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + 0.9090909091p + p2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + 0.9090909091p + p2 = 0 + 0.7272727273 0.9090909091p + p2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 0.9090909091p + p2 = 0.7272727273 The p term is 0.9090909091p. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091p + 0.2066115703 + p2 = 0.7272727273 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091p + p2 = 0.7272727273 + 0.2066115703 Combine like terms: 0.7272727273 + 0.2066115703 = 0.9338842976 0.2066115703 + 0.9090909091p + p2 = 0.9338842976 Factor a perfect square on the left side: (p + 0.4545454546)(p + 0.4545454546) = 0.9338842976 Calculate the square root of the right side: 0.966376892 Break this problem into two subproblems by setting (p + 0.4545454546) equal to 0.966376892 and -0.966376892.Subproblem 1
p + 0.4545454546 = 0.966376892 Simplifying p + 0.4545454546 = 0.966376892 Reorder the terms: 0.4545454546 + p = 0.966376892 Solving 0.4545454546 + p = 0.966376892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + p = 0.966376892 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + p = 0.966376892 + -0.4545454546 p = 0.966376892 + -0.4545454546 Combine like terms: 0.966376892 + -0.4545454546 = 0.5118314374 p = 0.5118314374 Simplifying p = 0.5118314374Subproblem 2
p + 0.4545454546 = -0.966376892 Simplifying p + 0.4545454546 = -0.966376892 Reorder the terms: 0.4545454546 + p = -0.966376892 Solving 0.4545454546 + p = -0.966376892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + p = -0.966376892 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + p = -0.966376892 + -0.4545454546 p = -0.966376892 + -0.4545454546 Combine like terms: -0.966376892 + -0.4545454546 = -1.4209223466 p = -1.4209223466 Simplifying p = -1.4209223466Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.5118314374, -1.4209223466}
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