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Simplifying 36x4 + -85x2 + -49 = 0 Reorder the terms: -49 + -85x2 + 36x4 = 0 Solving -49 + -85x2 + 36x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.361111111 + -2.361111111x2 + x4 = 0 Move the constant term to the right: Add '1.361111111' to each side of the equation. -1.361111111 + -2.361111111x2 + 1.361111111 + x4 = 0 + 1.361111111 Reorder the terms: -1.361111111 + 1.361111111 + -2.361111111x2 + x4 = 0 + 1.361111111 Combine like terms: -1.361111111 + 1.361111111 = 0.000000000 0.000000000 + -2.361111111x2 + x4 = 0 + 1.361111111 -2.361111111x2 + x4 = 0 + 1.361111111 Combine like terms: 0 + 1.361111111 = 1.361111111 -2.361111111x2 + x4 = 1.361111111 The x term is -2.361111111x2. Take half its coefficient (-1.180555556). Square it (1.393711421) and add it to both sides. Add '1.393711421' to each side of the equation. -2.361111111x2 + 1.393711421 + x4 = 1.361111111 + 1.393711421 Reorder the terms: 1.393711421 + -2.361111111x2 + x4 = 1.361111111 + 1.393711421 Combine like terms: 1.361111111 + 1.393711421 = 2.754822532 1.393711421 + -2.361111111x2 + x4 = 2.754822532 Factor a perfect square on the left side: (x2 + -1.180555556)(x2 + -1.180555556) = 2.754822532 Calculate the square root of the right side: 1.659765806 Break this problem into two subproblems by setting (x2 + -1.180555556) equal to 1.659765806 and -1.659765806.Subproblem 1
x2 + -1.180555556 = 1.659765806 Simplifying x2 + -1.180555556 = 1.659765806 Reorder the terms: -1.180555556 + x2 = 1.659765806 Solving -1.180555556 + x2 = 1.659765806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x2 = 1.659765806 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x2 = 1.659765806 + 1.180555556 x2 = 1.659765806 + 1.180555556 Combine like terms: 1.659765806 + 1.180555556 = 2.840321362 x2 = 2.840321362 Simplifying x2 = 2.840321362 Take the square root of each side: x = {-1.685325299, 1.685325299}Subproblem 2
x2 + -1.180555556 = -1.659765806 Simplifying x2 + -1.180555556 = -1.659765806 Reorder the terms: -1.180555556 + x2 = -1.659765806 Solving -1.180555556 + x2 = -1.659765806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.180555556' to each side of the equation. -1.180555556 + 1.180555556 + x2 = -1.659765806 + 1.180555556 Combine like terms: -1.180555556 + 1.180555556 = 0.000000000 0.000000000 + x2 = -1.659765806 + 1.180555556 x2 = -1.659765806 + 1.180555556 Combine like terms: -1.659765806 + 1.180555556 = -0.47921025 x2 = -0.47921025 Simplifying x2 = -0.47921025 Reorder the terms: 0.47921025 + x2 = -0.47921025 + 0.47921025 Combine like terms: -0.47921025 + 0.47921025 = 0.00000000 0.47921025 + 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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