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Simplifying 3.2x4 + -1.5x2 + -2.1 = 0 Reorder the terms: -2.1 + -1.5x2 + 3.2x4 = 0 Solving -2.1 + -1.5x2 + 3.2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -0.65625 + -0.46875x2 + x4 = 0 Move the constant term to the right: Add '0.65625' to each side of the equation. -0.65625 + -0.46875x2 + 0.65625 + x4 = 0 + 0.65625 Reorder the terms: -0.65625 + 0.65625 + -0.46875x2 + x4 = 0 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + -0.46875x2 + x4 = 0 + 0.65625 -0.46875x2 + x4 = 0 + 0.65625 Combine like terms: 0 + 0.65625 = 0.65625 -0.46875x2 + x4 = 0.65625 The x term is -0.46875x2. 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. -0.46875x2 + 0.05493164063 + x4 = 0.65625 + 0.05493164063 Reorder the terms: 0.05493164063 + -0.46875x2 + x4 = 0.65625 + 0.05493164063 Combine like terms: 0.65625 + 0.05493164063 = 0.71118164063 0.05493164063 + -0.46875x2 + x4 = 0.71118164063 Factor a perfect square on the left side: (x2 + -0.234375)(x2 + -0.234375) = 0.71118164063 Calculate the square root of the right side: 0.843315861 Break this problem into two subproblems by setting (x2 + -0.234375) equal to 0.843315861 and -0.843315861.Subproblem 1
x2 + -0.234375 = 0.843315861 Simplifying x2 + -0.234375 = 0.843315861 Reorder the terms: -0.234375 + x2 = 0.843315861 Solving -0.234375 + x2 = 0.843315861 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 + x2 = 0.843315861 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + x2 = 0.843315861 + 0.234375 x2 = 0.843315861 + 0.234375 Combine like terms: 0.843315861 + 0.234375 = 1.077690861 x2 = 1.077690861 Simplifying x2 = 1.077690861 Take the square root of each side: x = {-1.038118905, 1.038118905}Subproblem 2
x2 + -0.234375 = -0.843315861 Simplifying x2 + -0.234375 = -0.843315861 Reorder the terms: -0.234375 + x2 = -0.843315861 Solving -0.234375 + x2 = -0.843315861 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 + x2 = -0.843315861 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + x2 = -0.843315861 + 0.234375 x2 = -0.843315861 + 0.234375 Combine like terms: -0.843315861 + 0.234375 = -0.608940861 x2 = -0.608940861 Simplifying x2 = -0.608940861 Reorder the terms: 0.608940861 + x2 = -0.608940861 + 0.608940861 Combine like terms: -0.608940861 + 0.608940861 = 0.000000000 0.608940861 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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