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Simplifying 4x4 + -2x2 + -35 = 0 Reorder the terms: -35 + -2x2 + 4x4 = 0 Solving -35 + -2x2 + 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'. -8.75 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -0.5x2 + 8.75 + x4 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -0.5x2 + x4 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -0.5x2 + x4 = 0 + 8.75 -0.5x2 + x4 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -0.5x2 + x4 = 8.75 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 = 8.75 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 8.75 + 0.0625 Combine like terms: 8.75 + 0.0625 = 8.8125 0.0625 + -0.5x2 + x4 = 8.8125 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 8.8125 Calculate the square root of the right side: 2.968585522 Break this problem into two subproblems by setting (x2 + -0.25) equal to 2.968585522 and -2.968585522.Subproblem 1
x2 + -0.25 = 2.968585522 Simplifying x2 + -0.25 = 2.968585522 Reorder the terms: -0.25 + x2 = 2.968585522 Solving -0.25 + x2 = 2.968585522 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 = 2.968585522 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 2.968585522 + 0.25 x2 = 2.968585522 + 0.25 Combine like terms: 2.968585522 + 0.25 = 3.218585522 x2 = 3.218585522 Simplifying x2 = 3.218585522 Take the square root of each side: x = {-1.794041672, 1.794041672}Subproblem 2
x2 + -0.25 = -2.968585522 Simplifying x2 + -0.25 = -2.968585522 Reorder the terms: -0.25 + x2 = -2.968585522 Solving -0.25 + x2 = -2.968585522 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 = -2.968585522 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -2.968585522 + 0.25 x2 = -2.968585522 + 0.25 Combine like terms: -2.968585522 + 0.25 = -2.718585522 x2 = -2.718585522 Simplifying x2 = -2.718585522 Reorder the terms: 2.718585522 + x2 = -2.718585522 + 2.718585522 Combine like terms: -2.718585522 + 2.718585522 = 0.000000000 2.718585522 + 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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