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Simplifying -2x2 + -1x + -0.12 = 0 Reorder the terms: -0.12 + -1x + -2x2 = 0 Solving -0.12 + -1x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.06 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.06' to each side of the equation. 0.06 + 0.5x + -0.06 + x2 = 0 + -0.06 Reorder the terms: 0.06 + -0.06 + 0.5x + x2 = 0 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + 0.5x + x2 = 0 + -0.06 0.5x + x2 = 0 + -0.06 Combine like terms: 0 + -0.06 = -0.06 0.5x + x2 = -0.06 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.06 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.06 + 0.0625 Combine like terms: -0.06 + 0.0625 = 0.0025 0.0625 + 0.5x + x2 = 0.0025 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.0025 Calculate the square root of the right side: 0.05 Break this problem into two subproblems by setting (x + 0.25) equal to 0.05 and -0.05.Subproblem 1
x + 0.25 = 0.05 Simplifying x + 0.25 = 0.05 Reorder the terms: 0.25 + x = 0.05 Solving 0.25 + x = 0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.05 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.05 + -0.25 x = 0.05 + -0.25 Combine like terms: 0.05 + -0.25 = -0.2 x = -0.2 Simplifying x = -0.2Subproblem 2
x + 0.25 = -0.05 Simplifying x + 0.25 = -0.05 Reorder the terms: 0.25 + x = -0.05 Solving 0.25 + x = -0.05 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.05 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.05 + -0.25 x = -0.05 + -0.25 Combine like terms: -0.05 + -0.25 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2, -0.3}
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