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Simplifying 2x2 + -18x = -11 Reorder the terms: -18x + 2x2 = -11 Solving -18x + 2x2 = -11 Solving for variable 'x'. Reorder the terms: 11 + -18x + 2x2 = -11 + 11 Combine like terms: -11 + 11 = 0 11 + -18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -9x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -9x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -9x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -9x + x2 = 0 + -5.5 -9x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -9x + x2 = -5.5 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -5.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -5.5 + 20.25 Combine like terms: -5.5 + 20.25 = 14.75 20.25 + -9x + x2 = 14.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 14.75 Calculate the square root of the right side: 3.840572874 Break this problem into two subproblems by setting (x + -4.5) equal to 3.840572874 and -3.840572874.Subproblem 1
x + -4.5 = 3.840572874 Simplifying x + -4.5 = 3.840572874 Reorder the terms: -4.5 + x = 3.840572874 Solving -4.5 + x = 3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.840572874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.840572874 + 4.5 x = 3.840572874 + 4.5 Combine like terms: 3.840572874 + 4.5 = 8.340572874 x = 8.340572874 Simplifying x = 8.340572874Subproblem 2
x + -4.5 = -3.840572874 Simplifying x + -4.5 = -3.840572874 Reorder the terms: -4.5 + x = -3.840572874 Solving -4.5 + x = -3.840572874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.840572874 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.840572874 + 4.5 x = -3.840572874 + 4.5 Combine like terms: -3.840572874 + 4.5 = 0.659427126 x = 0.659427126 Simplifying x = 0.659427126Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.340572874, 0.659427126}
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