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Simplifying -0.2x2 + 0.1x = -0.02 Reorder the terms: 0.1x + -0.2x2 = -0.02 Solving 0.1x + -0.2x2 = -0.02 Solving for variable 'x'. Reorder the terms: 0.02 + 0.1x + -0.2x2 = -0.02 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.02 + 0.1x + -0.2x2 = 0.00 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -0.1 + -0.5x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.5x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.5x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.5x + x2 = 0.0 + 0.1 -0.5x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 -0.5x + x2 = 0.1 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 = 0.1 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.1 + 0.0625 Combine like terms: 0.1 + 0.0625 = 0.1625 0.0625 + -0.5x + x2 = 0.1625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.1625 Calculate the square root of the right side: 0.403112887 Break this problem into two subproblems by setting (x + -0.25) equal to 0.403112887 and -0.403112887.Subproblem 1
x + -0.25 = 0.403112887 Simplifying x + -0.25 = 0.403112887 Reorder the terms: -0.25 + x = 0.403112887 Solving -0.25 + x = 0.403112887 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 = 0.403112887 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.403112887 + 0.25 x = 0.403112887 + 0.25 Combine like terms: 0.403112887 + 0.25 = 0.653112887 x = 0.653112887 Simplifying x = 0.653112887Subproblem 2
x + -0.25 = -0.403112887 Simplifying x + -0.25 = -0.403112887 Reorder the terms: -0.25 + x = -0.403112887 Solving -0.25 + x = -0.403112887 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 = -0.403112887 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.403112887 + 0.25 x = -0.403112887 + 0.25 Combine like terms: -0.403112887 + 0.25 = -0.153112887 x = -0.153112887 Simplifying x = -0.153112887Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.653112887, -0.153112887}
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