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Simplifying 2x(x + -1) = 11 Reorder the terms: 2x(-1 + x) = 11 (-1 * 2x + x * 2x) = 11 (-2x + 2x2) = 11 Solving -2x + 2x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -2x + 2x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + -1x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + -1x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + -1x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + -1x + x2 = 0 + 5.5 -1x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 -1x + x2 = 5.5 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 = 5.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.5 + 0.25 Combine like terms: 5.5 + 0.25 = 5.75 0.25 + -1x + x2 = 5.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + -0.5) equal to 2.397915762 and -2.397915762.Subproblem 1
x + -0.5 = 2.397915762 Simplifying x + -0.5 = 2.397915762 Reorder the terms: -0.5 + x = 2.397915762 Solving -0.5 + x = 2.397915762 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 = 2.397915762 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.397915762 + 0.5 x = 2.397915762 + 0.5 Combine like terms: 2.397915762 + 0.5 = 2.897915762 x = 2.897915762 Simplifying x = 2.897915762Subproblem 2
x + -0.5 = -2.397915762 Simplifying x + -0.5 = -2.397915762 Reorder the terms: -0.5 + x = -2.397915762 Solving -0.5 + x = -2.397915762 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 = -2.397915762 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.397915762 + 0.5 x = -2.397915762 + 0.5 Combine like terms: -2.397915762 + 0.5 = -1.897915762 x = -1.897915762 Simplifying x = -1.897915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.897915762, -1.897915762}
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