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Simplifying 64x2 + -32x + -3 = 0 Reorder the terms: -3 + -32x + 64x2 = 0 Solving -3 + -32x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.046875 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.046875' to each side of the equation. -0.046875 + -0.5x + 0.046875 + x2 = 0 + 0.046875 Reorder the terms: -0.046875 + 0.046875 + -0.5x + x2 = 0 + 0.046875 Combine like terms: -0.046875 + 0.046875 = 0.000000 0.000000 + -0.5x + x2 = 0 + 0.046875 -0.5x + x2 = 0 + 0.046875 Combine like terms: 0 + 0.046875 = 0.046875 -0.5x + x2 = 0.046875 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 = 0.046875 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.046875 + 0.0625 Combine like terms: 0.046875 + 0.0625 = 0.109375 0.0625 + -0.5x + x2 = 0.109375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.109375 Calculate the square root of the right side: 0.330718914 Break this problem into two subproblems by setting (x + -0.25) equal to 0.330718914 and -0.330718914.Subproblem 1
x + -0.25 = 0.330718914 Simplifying x + -0.25 = 0.330718914 Reorder the terms: -0.25 + x = 0.330718914 Solving -0.25 + x = 0.330718914 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 = 0.330718914 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.330718914 + 0.25 x = 0.330718914 + 0.25 Combine like terms: 0.330718914 + 0.25 = 0.580718914 x = 0.580718914 Simplifying x = 0.580718914Subproblem 2
x + -0.25 = -0.330718914 Simplifying x + -0.25 = -0.330718914 Reorder the terms: -0.25 + x = -0.330718914 Solving -0.25 + x = -0.330718914 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 = -0.330718914 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.330718914 + 0.25 x = -0.330718914 + 0.25 Combine like terms: -0.330718914 + 0.25 = -0.080718914 x = -0.080718914 Simplifying x = -0.080718914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.580718914, -0.080718914}
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