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Simplifying 12x2 = x4 + -36 Reorder the terms: 12x2 = -36 + x4 Solving 12x2 = -36 + x4 Solving for variable 'x'. Reorder the terms: 36 + 12x2 + -1x4 = -36 + x4 + 36 + -1x4 Reorder the terms: 36 + 12x2 + -1x4 = -36 + 36 + x4 + -1x4 Combine like terms: -36 + 36 = 0 36 + 12x2 + -1x4 = 0 + x4 + -1x4 36 + 12x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 36 + 12x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -12x2 + x4 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -12x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -12x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12x2 + x4 = 0 + 36 -12x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -12x2 + x4 = 36 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 = 36 + 36 Reorder the terms: 36 + -12x2 + x4 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + -12x2 + x4 = 72 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x2 + -6) equal to 8.485281374 and -8.485281374.Subproblem 1
x2 + -6 = 8.485281374 Simplifying x2 + -6 = 8.485281374 Reorder the terms: -6 + x2 = 8.485281374 Solving -6 + x2 = 8.485281374 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 = 8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 8.485281374 + 6 x2 = 8.485281374 + 6 Combine like terms: 8.485281374 + 6 = 14.485281374 x2 = 14.485281374 Simplifying x2 = 14.485281374 Take the square root of each side: x = {-3.805953412, 3.805953412}Subproblem 2
x2 + -6 = -8.485281374 Simplifying x2 + -6 = -8.485281374 Reorder the terms: -6 + x2 = -8.485281374 Solving -6 + x2 = -8.485281374 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 = -8.485281374 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -8.485281374 + 6 x2 = -8.485281374 + 6 Combine like terms: -8.485281374 + 6 = -2.485281374 x2 = -2.485281374 Simplifying x2 = -2.485281374 Reorder the terms: 2.485281374 + x2 = -2.485281374 + 2.485281374 Combine like terms: -2.485281374 + 2.485281374 = 0.000000000 2.485281374 + 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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