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Simplifying x2 + -10x(x + -1) = -11 Reorder the terms: x2 + -10x(-1 + x) = -11 x2 + (-1 * -10x + x * -10x) = -11 x2 + (10x + -10x2) = -11 Reorder the terms: 10x + x2 + -10x2 = -11 Combine like terms: x2 + -10x2 = -9x2 10x + -9x2 = -11 Solving 10x + -9x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + 10x + -9x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + 10x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1.222222222 + -1.111111111x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + -1.111111111x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + -1.111111111x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + -1.111111111x + x2 = 0 + 1.222222222 -1.111111111x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 -1.111111111x + x2 = 1.222222222 The x term is -1.111111111x. Take half its coefficient (-0.5555555555). Square it (0.3086419752) and add it to both sides. Add '0.3086419752' to each side of the equation. -1.111111111x + 0.3086419752 + x2 = 1.222222222 + 0.3086419752 Reorder the terms: 0.3086419752 + -1.111111111x + x2 = 1.222222222 + 0.3086419752 Combine like terms: 1.222222222 + 0.3086419752 = 1.5308641972 0.3086419752 + -1.111111111x + x2 = 1.5308641972 Factor a perfect square on the left side: (x + -0.5555555555)(x + -0.5555555555) = 1.5308641972 Calculate the square root of the right side: 1.237280969 Break this problem into two subproblems by setting (x + -0.5555555555) equal to 1.237280969 and -1.237280969.Subproblem 1
x + -0.5555555555 = 1.237280969 Simplifying x + -0.5555555555 = 1.237280969 Reorder the terms: -0.5555555555 + x = 1.237280969 Solving -0.5555555555 + x = 1.237280969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 1.237280969 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 1.237280969 + 0.5555555555 x = 1.237280969 + 0.5555555555 Combine like terms: 1.237280969 + 0.5555555555 = 1.7928365245 x = 1.7928365245 Simplifying x = 1.7928365245Subproblem 2
x + -0.5555555555 = -1.237280969 Simplifying x + -0.5555555555 = -1.237280969 Reorder the terms: -0.5555555555 + x = -1.237280969 Solving -0.5555555555 + x = -1.237280969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -1.237280969 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -1.237280969 + 0.5555555555 x = -1.237280969 + 0.5555555555 Combine like terms: -1.237280969 + 0.5555555555 = -0.6817254135 x = -0.6817254135 Simplifying x = -0.6817254135Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7928365245, -0.6817254135}
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