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Simplifying 3x4 + -31x2 = 28 Reorder the terms: -31x2 + 3x4 = 28 Solving -31x2 + 3x4 = 28 Solving for variable 'x'. Reorder the terms: -28 + -31x2 + 3x4 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + -31x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -10.33333333x2 + x4 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -10.33333333x2 + 9.333333333 + x4 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -10.33333333x2 + x4 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -10.33333333x2 + x4 = 0 + 9.333333333 -10.33333333x2 + x4 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -10.33333333x2 + x4 = 9.333333333 The x term is -10.33333333x2. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x2 + 26.69444443 + x4 = 9.333333333 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x2 + x4 = 9.333333333 + 26.69444443 Combine like terms: 9.333333333 + 26.69444443 = 36.027777763 26.69444443 + -10.33333333x2 + x4 = 36.027777763 Factor a perfect square on the left side: (x2 + -5.166666665)(x2 + -5.166666665) = 36.027777763 Calculate the square root of the right side: 6.002314367 Break this problem into two subproblems by setting (x2 + -5.166666665) equal to 6.002314367 and -6.002314367.Subproblem 1
x2 + -5.166666665 = 6.002314367 Simplifying x2 + -5.166666665 = 6.002314367 Reorder the terms: -5.166666665 + x2 = 6.002314367 Solving -5.166666665 + x2 = 6.002314367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x2 = 6.002314367 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x2 = 6.002314367 + 5.166666665 x2 = 6.002314367 + 5.166666665 Combine like terms: 6.002314367 + 5.166666665 = 11.168981032 x2 = 11.168981032 Simplifying x2 = 11.168981032 Take the square root of each side: x = {-3.342002548, 3.342002548}Subproblem 2
x2 + -5.166666665 = -6.002314367 Simplifying x2 + -5.166666665 = -6.002314367 Reorder the terms: -5.166666665 + x2 = -6.002314367 Solving -5.166666665 + x2 = -6.002314367 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x2 = -6.002314367 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x2 = -6.002314367 + 5.166666665 x2 = -6.002314367 + 5.166666665 Combine like terms: -6.002314367 + 5.166666665 = -0.835647702 x2 = -0.835647702 Simplifying x2 = -0.835647702 Reorder the terms: 0.835647702 + x2 = -0.835647702 + 0.835647702 Combine like terms: -0.835647702 + 0.835647702 = 0.000000000 0.835647702 + 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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