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Simplifying 2x2 + -11x = -2 Reorder the terms: -11x + 2x2 = -2 Solving -11x + 2x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -11x + 2x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -5.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.5x + x2 = 0 + -1 -5.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.5x + x2 = -1 The x term is -5.5x. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5x + 7.5625 + x2 = -1 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = -1 + 7.5625 Combine like terms: -1 + 7.5625 = 6.5625 7.5625 + -5.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -2.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -2.75 = 2.561737691 Simplifying x + -2.75 = 2.561737691 Reorder the terms: -2.75 + x = 2.561737691 Solving -2.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 2.561737691 + 2.75 x = 2.561737691 + 2.75 Combine like terms: 2.561737691 + 2.75 = 5.311737691 x = 5.311737691 Simplifying x = 5.311737691Subproblem 2
x + -2.75 = -2.561737691 Simplifying x + -2.75 = -2.561737691 Reorder the terms: -2.75 + x = -2.561737691 Solving -2.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -2.561737691 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -2.561737691 + 2.75 x = -2.561737691 + 2.75 Combine like terms: -2.561737691 + 2.75 = 0.188262309 x = 0.188262309 Simplifying x = 0.188262309Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.311737691, 0.188262309}
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