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Simplifying 0 = 6x4 + -3x2 + -1 Reorder the terms: 0 = -1 + -3x2 + 6x4 Solving 0 = -1 + -3x2 + 6x4 Solving for variable 'x'. Combine like terms: 0 + 1 = 1 1 + 3x2 + -6x4 = -1 + -3x2 + 6x4 + 1 + 3x2 + -6x4 Reorder the terms: 1 + 3x2 + -6x4 = -1 + 1 + -3x2 + 3x2 + 6x4 + -6x4 Combine like terms: -1 + 1 = 0 1 + 3x2 + -6x4 = 0 + -3x2 + 3x2 + 6x4 + -6x4 1 + 3x2 + -6x4 = -3x2 + 3x2 + 6x4 + -6x4 Combine like terms: -3x2 + 3x2 = 0 1 + 3x2 + -6x4 = 0 + 6x4 + -6x4 1 + 3x2 + -6x4 = 6x4 + -6x4 Combine like terms: 6x4 + -6x4 = 0 1 + 3x2 + -6x4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.5x2 + 0.1666666667 + x4 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.5x2 + x4 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.5x2 + x4 = 0 + 0.1666666667 -0.5x2 + x4 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.5x2 + x4 = 0.1666666667 The x term is -0.5x2. 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. -0.5x2 + 0.0625 + x4 = 0.1666666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 0.1666666667 + 0.0625 Combine like terms: 0.1666666667 + 0.0625 = 0.2291666667 0.0625 + -0.5x2 + x4 = 0.2291666667 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 0.2291666667 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x2 + -0.25) equal to 0.478713554 and -0.478713554.Subproblem 1
x2 + -0.25 = 0.478713554 Simplifying x2 + -0.25 = 0.478713554 Reorder the terms: -0.25 + x2 = 0.478713554 Solving -0.25 + x2 = 0.478713554 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 + x2 = 0.478713554 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 0.478713554 + 0.25 x2 = 0.478713554 + 0.25 Combine like terms: 0.478713554 + 0.25 = 0.728713554 x2 = 0.728713554 Simplifying x2 = 0.728713554 Take the square root of each side: x = {-0.853647207, 0.853647207}Subproblem 2
x2 + -0.25 = -0.478713554 Simplifying x2 + -0.25 = -0.478713554 Reorder the terms: -0.25 + x2 = -0.478713554 Solving -0.25 + x2 = -0.478713554 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 + x2 = -0.478713554 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -0.478713554 + 0.25 x2 = -0.478713554 + 0.25 Combine like terms: -0.478713554 + 0.25 = -0.228713554 x2 = -0.228713554 Simplifying x2 = -0.228713554 Reorder the terms: 0.228713554 + x2 = -0.228713554 + 0.228713554 Combine like terms: -0.228713554 + 0.228713554 = 0.000000000 0.228713554 + 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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