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Simplifying 2x2 + -4x = 1.33333 Reorder the terms: -4x + 2x2 = 1.33333 Solving -4x + 2x2 = 1.33333 Solving for variable 'x'. Reorder the terms: -1.33333 + -4x + 2x2 = 1.33333 + -1.33333 Combine like terms: 1.33333 + -1.33333 = 0.00000 -1.33333 + -4x + 2x2 = 0.00000 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.666665 + -2x + x2 = 0.00000 Move the constant term to the right: Add '0.666665' to each side of the equation. -0.666665 + -2x + 0.666665 + x2 = 0.00000 + 0.666665 Reorder the terms: -0.666665 + 0.666665 + -2x + x2 = 0.00000 + 0.666665 Combine like terms: -0.666665 + 0.666665 = 0.000000 0.000000 + -2x + x2 = 0.00000 + 0.666665 -2x + x2 = 0.00000 + 0.666665 Combine like terms: 0.00000 + 0.666665 = 0.666665 -2x + x2 = 0.666665 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.666665 + 1 Reorder the terms: 1 + -2x + x2 = 0.666665 + 1 Combine like terms: 0.666665 + 1 = 1.666665 1 + -2x + x2 = 1.666665 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.666665 Calculate the square root of the right side: 1.290993803 Break this problem into two subproblems by setting (x + -1) equal to 1.290993803 and -1.290993803.Subproblem 1
x + -1 = 1.290993803 Simplifying x + -1 = 1.290993803 Reorder the terms: -1 + x = 1.290993803 Solving -1 + x = 1.290993803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.290993803 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.290993803 + 1 x = 1.290993803 + 1 Combine like terms: 1.290993803 + 1 = 2.290993803 x = 2.290993803 Simplifying x = 2.290993803Subproblem 2
x + -1 = -1.290993803 Simplifying x + -1 = -1.290993803 Reorder the terms: -1 + x = -1.290993803 Solving -1 + x = -1.290993803 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.290993803 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.290993803 + 1 x = -1.290993803 + 1 Combine like terms: -1.290993803 + 1 = -0.290993803 x = -0.290993803 Simplifying x = -0.290993803Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.290993803, -0.290993803}
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