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Simplifying 27 = x4 + -12x2 Reorder the terms: 27 = -12x2 + x4 Solving 27 = -12x2 + x4 Solving for variable 'x'. Reorder the terms: 27 + 12x2 + -1x4 = -12x2 + 12x2 + x4 + -1x4 Combine like terms: -12x2 + 12x2 = 0 27 + 12x2 + -1x4 = 0 + x4 + -1x4 27 + 12x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 27 + 12x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -12x2 + x4 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -12x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + -12x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -12x2 + x4 = 0 + 27 -12x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 -12x2 + x4 = 27 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 = 27 + 36 Reorder the terms: 36 + -12x2 + x4 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + -12x2 + x4 = 63 Factor a perfect square on the left side: (x2 + -6)(x2 + -6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x2 + -6) equal to 7.937253933 and -7.937253933.Subproblem 1
x2 + -6 = 7.937253933 Simplifying x2 + -6 = 7.937253933 Reorder the terms: -6 + x2 = 7.937253933 Solving -6 + x2 = 7.937253933 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 = 7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = 7.937253933 + 6 x2 = 7.937253933 + 6 Combine like terms: 7.937253933 + 6 = 13.937253933 x2 = 13.937253933 Simplifying x2 = 13.937253933 Take the square root of each side: x = {-3.733263175, 3.733263175}Subproblem 2
x2 + -6 = -7.937253933 Simplifying x2 + -6 = -7.937253933 Reorder the terms: -6 + x2 = -7.937253933 Solving -6 + x2 = -7.937253933 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 = -7.937253933 + 6 Combine like terms: -6 + 6 = 0 0 + x2 = -7.937253933 + 6 x2 = -7.937253933 + 6 Combine like terms: -7.937253933 + 6 = -1.937253933 x2 = -1.937253933 Simplifying x2 = -1.937253933 Reorder the terms: 1.937253933 + x2 = -1.937253933 + 1.937253933 Combine like terms: -1.937253933 + 1.937253933 = 0.000000000 1.937253933 + 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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