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Simplifying 32x2 + -4x + -2 = 0 Reorder the terms: -2 + -4x + 32x2 = 0 Solving -2 + -4x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -2x + 16x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2x + 16x2)' equal to zero and attempt to solve: Simplifying -1 + -2x + 16x2 = 0 Solving -1 + -2x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.125x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.125x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.125x + x2 = 0 + 0.0625 -0.125x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.125x + x2 = 0.0625 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.0625 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.0625 + 0.00390625 Combine like terms: 0.0625 + 0.00390625 = 0.06640625 0.00390625 + -0.125x + x2 = 0.06640625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.06640625 Calculate the square root of the right side: 0.257694102 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.257694102 and -0.257694102.Subproblem 1
x + -0.0625 = 0.257694102 Simplifying x + -0.0625 = 0.257694102 Reorder the terms: -0.0625 + x = 0.257694102 Solving -0.0625 + x = 0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.257694102 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.257694102 + 0.0625 x = 0.257694102 + 0.0625 Combine like terms: 0.257694102 + 0.0625 = 0.320194102 x = 0.320194102 Simplifying x = 0.320194102Subproblem 2
x + -0.0625 = -0.257694102 Simplifying x + -0.0625 = -0.257694102 Reorder the terms: -0.0625 + x = -0.257694102 Solving -0.0625 + x = -0.257694102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.257694102 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.257694102 + 0.0625 x = -0.257694102 + 0.0625 Combine like terms: -0.257694102 + 0.0625 = -0.195194102 x = -0.195194102 Simplifying x = -0.195194102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.320194102, -0.195194102}Solution
x = {0.320194102, -0.195194102}
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