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Simplifying 2x2 + -2x + 1 = 14 Reorder the terms: 1 + -2x + 2x2 = 14 Solving 1 + -2x + 2x2 = 14 Solving for variable 'x'. Reorder the terms: 1 + -14 + -2x + 2x2 = 14 + -14 Combine like terms: 1 + -14 = -13 -13 + -2x + 2x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -13 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6.5 + -1x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1x + x2 = 0 + 6.5 -1x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1x + x2 = 6.5 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 = 6.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.5 + 0.25 Combine like terms: 6.5 + 0.25 = 6.75 0.25 + -1x + x2 = 6.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -0.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -0.5 = 2.598076211 Simplifying x + -0.5 = 2.598076211 Reorder the terms: -0.5 + x = 2.598076211 Solving -0.5 + x = 2.598076211 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 = 2.598076211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.598076211 + 0.5 x = 2.598076211 + 0.5 Combine like terms: 2.598076211 + 0.5 = 3.098076211 x = 3.098076211 Simplifying x = 3.098076211Subproblem 2
x + -0.5 = -2.598076211 Simplifying x + -0.5 = -2.598076211 Reorder the terms: -0.5 + x = -2.598076211 Solving -0.5 + x = -2.598076211 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 = -2.598076211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.598076211 + 0.5 x = -2.598076211 + 0.5 Combine like terms: -2.598076211 + 0.5 = -2.098076211 x = -2.098076211 Simplifying x = -2.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.098076211, -2.098076211}
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