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Simplifying 2x + -2x2 = 0.28 Solving 2x + -2x2 = 0.28 Solving for variable 'x'. Reorder the terms: -0.28 + 2x + -2x2 = 0.28 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 -0.28 + 2x + -2x2 = 0.00 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.14 + -1x + x2 = 0.00 Move the constant term to the right: Add '-0.14' to each side of the equation. 0.14 + -1x + -0.14 + x2 = 0.00 + -0.14 Reorder the terms: 0.14 + -0.14 + -1x + x2 = 0.00 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + -1x + x2 = 0.00 + -0.14 -1x + x2 = 0.00 + -0.14 Combine like terms: 0.00 + -0.14 = -0.14 -1x + x2 = -0.14 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 = -0.14 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.14 + 0.25 Combine like terms: -0.14 + 0.25 = 0.11 0.25 + -1x + x2 = 0.11 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.11 Calculate the square root of the right side: 0.331662479 Break this problem into two subproblems by setting (x + -0.5) equal to 0.331662479 and -0.331662479.Subproblem 1
x + -0.5 = 0.331662479 Simplifying x + -0.5 = 0.331662479 Reorder the terms: -0.5 + x = 0.331662479 Solving -0.5 + x = 0.331662479 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 = 0.331662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.331662479 + 0.5 x = 0.331662479 + 0.5 Combine like terms: 0.331662479 + 0.5 = 0.831662479 x = 0.831662479 Simplifying x = 0.831662479Subproblem 2
x + -0.5 = -0.331662479 Simplifying x + -0.5 = -0.331662479 Reorder the terms: -0.5 + x = -0.331662479 Solving -0.5 + x = -0.331662479 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 = -0.331662479 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.331662479 + 0.5 x = -0.331662479 + 0.5 Combine like terms: -0.331662479 + 0.5 = 0.168337521 x = 0.168337521 Simplifying x = 0.168337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.831662479, 0.168337521}
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