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Simplifying 3x4 + -10x2 + -108 = 0 Reorder the terms: -108 + -10x2 + 3x4 = 0 Solving -108 + -10x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -36 + -3.333333333x2 + x4 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -3.333333333x2 + 36 + x4 = 0 + 36 Reorder the terms: -36 + 36 + -3.333333333x2 + x4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -3.333333333x2 + x4 = 0 + 36 -3.333333333x2 + x4 = 0 + 36 Combine like terms: 0 + 36 = 36 -3.333333333x2 + x4 = 36 The x term is -3.333333333x2. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x2 + 2.777777779 + x4 = 36 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x2 + x4 = 36 + 2.777777779 Combine like terms: 36 + 2.777777779 = 38.777777779 2.777777779 + -3.333333333x2 + x4 = 38.777777779 Factor a perfect square on the left side: (x2 + -1.666666667)(x2 + -1.666666667) = 38.777777779 Calculate the square root of the right side: 6.227180564 Break this problem into two subproblems by setting (x2 + -1.666666667) equal to 6.227180564 and -6.227180564.Subproblem 1
x2 + -1.666666667 = 6.227180564 Simplifying x2 + -1.666666667 = 6.227180564 Reorder the terms: -1.666666667 + x2 = 6.227180564 Solving -1.666666667 + x2 = 6.227180564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x2 = 6.227180564 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = 6.227180564 + 1.666666667 x2 = 6.227180564 + 1.666666667 Combine like terms: 6.227180564 + 1.666666667 = 7.893847231 x2 = 7.893847231 Simplifying x2 = 7.893847231 Take the square root of each side: x = {-2.809599123, 2.809599123}Subproblem 2
x2 + -1.666666667 = -6.227180564 Simplifying x2 + -1.666666667 = -6.227180564 Reorder the terms: -1.666666667 + x2 = -6.227180564 Solving -1.666666667 + x2 = -6.227180564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x2 = -6.227180564 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = -6.227180564 + 1.666666667 x2 = -6.227180564 + 1.666666667 Combine like terms: -6.227180564 + 1.666666667 = -4.560513897 x2 = -4.560513897 Simplifying x2 = -4.560513897 Reorder the terms: 4.560513897 + x2 = -4.560513897 + 4.560513897 Combine like terms: -4.560513897 + 4.560513897 = 0.000000000 4.560513897 + 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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