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Simplifying -0.2x2 + 0.1x = -0.06 Reorder the terms: 0.1x + -0.2x2 = -0.06 Solving 0.1x + -0.2x2 = -0.06 Solving for variable 'x'. Reorder the terms: 0.06 + 0.1x + -0.2x2 = -0.06 + 0.06 Combine like terms: -0.06 + 0.06 = 0.00 0.06 + 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'. -0.3 + -0.5x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + -0.5x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + -0.5x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + -0.5x + x2 = 0.0 + 0.3 -0.5x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 -0.5x + x2 = 0.3 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 = 0.3 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.3 + 0.0625 Combine like terms: 0.3 + 0.0625 = 0.3625 0.0625 + -0.5x + x2 = 0.3625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x + -0.25) equal to 0.602079729 and -0.602079729.Subproblem 1
x + -0.25 = 0.602079729 Simplifying x + -0.25 = 0.602079729 Reorder the terms: -0.25 + x = 0.602079729 Solving -0.25 + x = 0.602079729 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 = 0.602079729 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.602079729 + 0.25 x = 0.602079729 + 0.25 Combine like terms: 0.602079729 + 0.25 = 0.852079729 x = 0.852079729 Simplifying x = 0.852079729Subproblem 2
x + -0.25 = -0.602079729 Simplifying x + -0.25 = -0.602079729 Reorder the terms: -0.25 + x = -0.602079729 Solving -0.25 + x = -0.602079729 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 = -0.602079729 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.602079729 + 0.25 x = -0.602079729 + 0.25 Combine like terms: -0.602079729 + 0.25 = -0.352079729 x = -0.352079729 Simplifying x = -0.352079729Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.852079729, -0.352079729}
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