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Simplifying -0.2x2 + 0.1x + 1 = 0 Reorder the terms: 1 + 0.1x + -0.2x2 = 0 Solving 1 + 0.1x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -5 + -0.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.5x + x2 = 0 + 5 -0.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.5x + x2 = 5 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 = 5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 5 + 0.0625 Combine like terms: 5 + 0.0625 = 5.0625 0.0625 + -0.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -0.25) equal to 2.25 and -2.25.Subproblem 1
x + -0.25 = 2.25 Simplifying x + -0.25 = 2.25 Reorder the terms: -0.25 + x = 2.25 Solving -0.25 + x = 2.25 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 = 2.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.25 + 0.25 x = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 x = 2.5 Simplifying x = 2.5Subproblem 2
x + -0.25 = -2.25 Simplifying x + -0.25 = -2.25 Reorder the terms: -0.25 + x = -2.25 Solving -0.25 + x = -2.25 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 = -2.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.25 + 0.25 x = -2.25 + 0.25 Combine like terms: -2.25 + 0.25 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5, -2}
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