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Simplifying 0.25x2 + -0.08x + -0.83 = 0 Reorder the terms: -0.83 + -0.08x + 0.25x2 = 0 Solving -0.83 + -0.08x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -3.32 + -0.32x + x2 = 0 Move the constant term to the right: Add '3.32' to each side of the equation. -3.32 + -0.32x + 3.32 + x2 = 0 + 3.32 Reorder the terms: -3.32 + 3.32 + -0.32x + x2 = 0 + 3.32 Combine like terms: -3.32 + 3.32 = 0.00 0.00 + -0.32x + x2 = 0 + 3.32 -0.32x + x2 = 0 + 3.32 Combine like terms: 0 + 3.32 = 3.32 -0.32x + x2 = 3.32 The x term is -0.32x. Take half its coefficient (-0.16). Square it (0.0256) and add it to both sides. Add '0.0256' to each side of the equation. -0.32x + 0.0256 + x2 = 3.32 + 0.0256 Reorder the terms: 0.0256 + -0.32x + x2 = 3.32 + 0.0256 Combine like terms: 3.32 + 0.0256 = 3.3456 0.0256 + -0.32x + x2 = 3.3456 Factor a perfect square on the left side: (x + -0.16)(x + -0.16) = 3.3456 Calculate the square root of the right side: 1.829098138 Break this problem into two subproblems by setting (x + -0.16) equal to 1.829098138 and -1.829098138.Subproblem 1
x + -0.16 = 1.829098138 Simplifying x + -0.16 = 1.829098138 Reorder the terms: -0.16 + x = 1.829098138 Solving -0.16 + x = 1.829098138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.16' to each side of the equation. -0.16 + 0.16 + x = 1.829098138 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + x = 1.829098138 + 0.16 x = 1.829098138 + 0.16 Combine like terms: 1.829098138 + 0.16 = 1.989098138 x = 1.989098138 Simplifying x = 1.989098138Subproblem 2
x + -0.16 = -1.829098138 Simplifying x + -0.16 = -1.829098138 Reorder the terms: -0.16 + x = -1.829098138 Solving -0.16 + x = -1.829098138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.16' to each side of the equation. -0.16 + 0.16 + x = -1.829098138 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + x = -1.829098138 + 0.16 x = -1.829098138 + 0.16 Combine like terms: -1.829098138 + 0.16 = -1.669098138 x = -1.669098138 Simplifying x = -1.669098138Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.989098138, -1.669098138}
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