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Simplifying 4x4 + -3x2 + -2 = 0 Reorder the terms: -2 + -3x2 + 4x4 = 0 Solving -2 + -3x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -0.75x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.75x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.75x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.75x2 + x4 = 0 + 0.5 -0.75x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.75x2 + x4 = 0.5 The x term is -0.75x2. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x2 + 0.140625 + x4 = 0.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x2 + x4 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + -0.75x2 + x4 = 0.640625 Factor a perfect square on the left side: (x2 + -0.375)(x2 + -0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x2 + -0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
x2 + -0.375 = 0.80039053 Simplifying x2 + -0.375 = 0.80039053 Reorder the terms: -0.375 + x2 = 0.80039053 Solving -0.375 + x2 = 0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x2 = 0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = 0.80039053 + 0.375 x2 = 0.80039053 + 0.375 Combine like terms: 0.80039053 + 0.375 = 1.17539053 x2 = 1.17539053 Simplifying x2 = 1.17539053 Take the square root of each side: x = {-1.084154293, 1.084154293}Subproblem 2
x2 + -0.375 = -0.80039053 Simplifying x2 + -0.375 = -0.80039053 Reorder the terms: -0.375 + x2 = -0.80039053 Solving -0.375 + x2 = -0.80039053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x2 = -0.80039053 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = -0.80039053 + 0.375 x2 = -0.80039053 + 0.375 Combine like terms: -0.80039053 + 0.375 = -0.42539053 x2 = -0.42539053 Simplifying x2 = -0.42539053 Reorder the terms: 0.42539053 + x2 = -0.42539053 + 0.42539053 Combine like terms: -0.42539053 + 0.42539053 = 0.00000000 0.42539053 + x2 = 0.00000000 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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