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Simplifying x * -10(x + -1) = -11 Reorder the terms: x * -10(-1 + x) = -11 Reorder the terms for easier multiplication: -10x(-1 + x) = -11 (-1 * -10x + x * -10x) = -11 (10x + -10x2) = -11 Solving 10x + -10x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + 10x + -10x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + 10x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.1 + -1x + x2 = 0 Move the constant term to the right: Add '1.1' to each side of the equation. -1.1 + -1x + 1.1 + x2 = 0 + 1.1 Reorder the terms: -1.1 + 1.1 + -1x + x2 = 0 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + -1x + x2 = 0 + 1.1 -1x + x2 = 0 + 1.1 Combine like terms: 0 + 1.1 = 1.1 -1x + x2 = 1.1 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.1 + 0.25 Combine like terms: 1.1 + 0.25 = 1.35 0.25 + -1x + x2 = 1.35 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.35 Calculate the square root of the right side: 1.161895004 Break this problem into two subproblems by setting (x + -0.5) equal to 1.161895004 and -1.161895004.Subproblem 1
x + -0.5 = 1.161895004 Simplifying x + -0.5 = 1.161895004 Reorder the terms: -0.5 + x = 1.161895004 Solving -0.5 + x = 1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.161895004 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.161895004 + 0.5 x = 1.161895004 + 0.5 Combine like terms: 1.161895004 + 0.5 = 1.661895004 x = 1.661895004 Simplifying x = 1.661895004Subproblem 2
x + -0.5 = -1.161895004 Simplifying x + -0.5 = -1.161895004 Reorder the terms: -0.5 + x = -1.161895004 Solving -0.5 + x = -1.161895004 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.161895004 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.161895004 + 0.5 x = -1.161895004 + 0.5 Combine like terms: -1.161895004 + 0.5 = -0.661895004 x = -0.661895004 Simplifying x = -0.661895004Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.661895004, -0.661895004}
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