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Simplifying x4 + 12x2 = 35 Reorder the terms: 12x2 + x4 = 35 Solving 12x2 + x4 = 35 Solving for variable 'x'. Reorder the terms: -35 + 12x2 + x4 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 12x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 12x2 + 35 + x4 = 0 + 35 Reorder the terms: -35 + 35 + 12x2 + x4 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 12x2 + x4 = 0 + 35 12x2 + x4 = 0 + 35 Combine like terms: 0 + 35 = 35 12x2 + x4 = 35 The x term is 12x2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x2 + 36 + x4 = 35 + 36 Reorder the terms: 36 + 12x2 + x4 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + 12x2 + x4 = 71 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x2 + 6) equal to 8.426149773 and -8.426149773.Subproblem 1
x2 + 6 = 8.426149773 Simplifying x2 + 6 = 8.426149773 Reorder the terms: 6 + x2 = 8.426149773 Solving 6 + x2 = 8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 8.426149773 + -6 x2 = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 x2 = 2.426149773 Simplifying x2 = 2.426149773 Take the square root of each side: x = {-1.557610276, 1.557610276}Subproblem 2
x2 + 6 = -8.426149773 Simplifying x2 + 6 = -8.426149773 Reorder the terms: 6 + x2 = -8.426149773 Solving 6 + x2 = -8.426149773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -8.426149773 + -6 x2 = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 x2 = -14.426149773 Simplifying x2 = -14.426149773 Reorder the terms: 14.426149773 + x2 = -14.426149773 + 14.426149773 Combine like terms: -14.426149773 + 14.426149773 = 0.000000000 14.426149773 + 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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