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Simplifying 0.625x2 + -0.125x + -1 = 0 Reorder the terms: -1 + -0.125x + 0.625x2 = 0 Solving -1 + -0.125x + 0.625x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.625 the coefficient of the squared term: Divide each side by '0.625'. -1.6 + -0.2x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.2x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.2x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.2x + x2 = 0 + 1.6 -0.2x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.2x + x2 = 1.6 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 1.6 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 1.6 + 0.01 Combine like terms: 1.6 + 0.01 = 1.61 0.01 + -0.2x + x2 = 1.61 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + -0.1) equal to 1.268857754 and -1.268857754.Subproblem 1
x + -0.1 = 1.268857754 Simplifying x + -0.1 = 1.268857754 Reorder the terms: -0.1 + x = 1.268857754 Solving -0.1 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.268857754 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.268857754 + 0.1 x = 1.268857754 + 0.1 Combine like terms: 1.268857754 + 0.1 = 1.368857754 x = 1.368857754 Simplifying x = 1.368857754Subproblem 2
x + -0.1 = -1.268857754 Simplifying x + -0.1 = -1.268857754 Reorder the terms: -0.1 + x = -1.268857754 Solving -0.1 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.268857754 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.268857754 + 0.1 x = -1.268857754 + 0.1 Combine like terms: -1.268857754 + 0.1 = -1.168857754 x = -1.168857754 Simplifying x = -1.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.368857754, -1.168857754}
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