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Simplifying 0.3x + -0.01 = -0.64x2 Reorder the terms: -0.01 + 0.3x = -0.64x2 Solving -0.01 + 0.3x = -0.64x2 Solving for variable 'x'. Combine like terms: -0.64x2 + 0.64x2 = 0.00 -0.01 + 0.3x + 0.64x2 = 0.00 Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -0.015625 + 0.46875x + x2 = 0 Move the constant term to the right: Add '0.015625' to each side of the equation. -0.015625 + 0.46875x + 0.015625 + x2 = 0 + 0.015625 Reorder the terms: -0.015625 + 0.015625 + 0.46875x + x2 = 0 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + 0.46875x + x2 = 0 + 0.015625 0.46875x + x2 = 0 + 0.015625 Combine like terms: 0 + 0.015625 = 0.015625 0.46875x + x2 = 0.015625 The x term is 0.46875x. Take half its coefficient (0.234375). Square it (0.05493164063) and add it to both sides. Add '0.05493164063' to each side of the equation. 0.46875x + 0.05493164063 + x2 = 0.015625 + 0.05493164063 Reorder the terms: 0.05493164063 + 0.46875x + x2 = 0.015625 + 0.05493164063 Combine like terms: 0.015625 + 0.05493164063 = 0.07055664063 0.05493164063 + 0.46875x + x2 = 0.07055664063 Factor a perfect square on the left side: (x + 0.234375)(x + 0.234375) = 0.07055664063 Calculate the square root of the right side: 0.265625 Break this problem into two subproblems by setting (x + 0.234375) equal to 0.265625 and -0.265625.Subproblem 1
x + 0.234375 = 0.265625 Simplifying x + 0.234375 = 0.265625 Reorder the terms: 0.234375 + x = 0.265625 Solving 0.234375 + x = 0.265625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + x = 0.265625 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + x = 0.265625 + -0.234375 x = 0.265625 + -0.234375 Combine like terms: 0.265625 + -0.234375 = 0.03125 x = 0.03125 Simplifying x = 0.03125Subproblem 2
x + 0.234375 = -0.265625 Simplifying x + 0.234375 = -0.265625 Reorder the terms: 0.234375 + x = -0.265625 Solving 0.234375 + x = -0.265625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.234375' to each side of the equation. 0.234375 + -0.234375 + x = -0.265625 + -0.234375 Combine like terms: 0.234375 + -0.234375 = 0.000000 0.000000 + x = -0.265625 + -0.234375 x = -0.265625 + -0.234375 Combine like terms: -0.265625 + -0.234375 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03125, -0.5}
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