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Simplifying -4x4 + x2 + -10 + 12x4 + -7x2 = 0 Reorder the terms: -10 + x2 + -7x2 + -4x4 + 12x4 = 0 Combine like terms: x2 + -7x2 = -6x2 -10 + -6x2 + -4x4 + 12x4 = 0 Combine like terms: -4x4 + 12x4 = 8x4 -10 + -6x2 + 8x4 = 0 Solving -10 + -6x2 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -3x2 + 4x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -3x2 + 4x4)' equal to zero and attempt to solve: Simplifying -5 + -3x2 + 4x4 = 0 Solving -5 + -3x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -0.75x2 + x4 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.75x2 + 1.25 + x4 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.75x2 + x4 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.75x2 + x4 = 0 + 1.25 -0.75x2 + x4 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.75x2 + x4 = 1.25 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 = 1.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x2 + x4 = 1.25 + 0.140625 Combine like terms: 1.25 + 0.140625 = 1.390625 0.140625 + -0.75x2 + x4 = 1.390625 Factor a perfect square on the left side: (x2 + -0.375)(x2 + -0.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x2 + -0.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x2 + -0.375 = 1.179247642 Simplifying x2 + -0.375 = 1.179247642 Reorder the terms: -0.375 + x2 = 1.179247642 Solving -0.375 + x2 = 1.179247642 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 = 1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = 1.179247642 + 0.375 x2 = 1.179247642 + 0.375 Combine like terms: 1.179247642 + 0.375 = 1.554247642 x2 = 1.554247642 Simplifying x2 = 1.554247642 Take the square root of each side: x = {-1.246694687, 1.246694687}Subproblem 2
x2 + -0.375 = -1.179247642 Simplifying x2 + -0.375 = -1.179247642 Reorder the terms: -0.375 + x2 = -1.179247642 Solving -0.375 + x2 = -1.179247642 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 = -1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x2 = -1.179247642 + 0.375 x2 = -1.179247642 + 0.375 Combine like terms: -1.179247642 + 0.375 = -0.804247642 x2 = -0.804247642 Simplifying x2 = -0.804247642 Reorder the terms: 0.804247642 + x2 = -0.804247642 + 0.804247642 Combine like terms: -0.804247642 + 0.804247642 = 0.000000000 0.804247642 + 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. 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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