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Simplifying 1 + 12x2 + x4 = 0 Solving 1 + 12x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 12x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + 12x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 12x2 + x4 = 0 + -1 12x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 12x2 + x4 = -1 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 = -1 + 36 Reorder the terms: 36 + 12x2 + x4 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + 12x2 + x4 = 35 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x2 + 6) equal to 5.916079783 and -5.916079783.Subproblem 1
x2 + 6 = 5.916079783 Simplifying x2 + 6 = 5.916079783 Reorder the terms: 6 + x2 = 5.916079783 Solving 6 + x2 = 5.916079783 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 = 5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 5.916079783 + -6 x2 = 5.916079783 + -6 Combine like terms: 5.916079783 + -6 = -0.083920217 x2 = -0.083920217 Simplifying x2 = -0.083920217 Reorder the terms: 0.083920217 + x2 = -0.083920217 + 0.083920217 Combine like terms: -0.083920217 + 0.083920217 = 0.000000000 0.083920217 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 6 = -5.916079783 Simplifying x2 + 6 = -5.916079783 Reorder the terms: 6 + x2 = -5.916079783 Solving 6 + x2 = -5.916079783 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 = -5.916079783 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -5.916079783 + -6 x2 = -5.916079783 + -6 Combine like terms: -5.916079783 + -6 = -11.916079783 x2 = -11.916079783 Simplifying x2 = -11.916079783 Reorder the terms: 11.916079783 + x2 = -11.916079783 + 11.916079783 Combine like terms: -11.916079783 + 11.916079783 = 0.000000000 11.916079783 + 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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