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Simplifying 3x4 + -10x2 + -45 = 0 Reorder the terms: -45 + -10x2 + 3x4 = 0 Solving -45 + -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'. -15 + -3.333333333x2 + x4 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -3.333333333x2 + 15 + x4 = 0 + 15 Reorder the terms: -15 + 15 + -3.333333333x2 + x4 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3.333333333x2 + x4 = 0 + 15 -3.333333333x2 + x4 = 0 + 15 Combine like terms: 0 + 15 = 15 -3.333333333x2 + x4 = 15 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 = 15 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x2 + x4 = 15 + 2.777777779 Combine like terms: 15 + 2.777777779 = 17.777777779 2.777777779 + -3.333333333x2 + x4 = 17.777777779 Factor a perfect square on the left side: (x2 + -1.666666667)(x2 + -1.666666667) = 17.777777779 Calculate the square root of the right side: 4.216370214 Break this problem into two subproblems by setting (x2 + -1.666666667) equal to 4.216370214 and -4.216370214.Subproblem 1
x2 + -1.666666667 = 4.216370214 Simplifying x2 + -1.666666667 = 4.216370214 Reorder the terms: -1.666666667 + x2 = 4.216370214 Solving -1.666666667 + x2 = 4.216370214 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 = 4.216370214 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = 4.216370214 + 1.666666667 x2 = 4.216370214 + 1.666666667 Combine like terms: 4.216370214 + 1.666666667 = 5.883036881 x2 = 5.883036881 Simplifying x2 = 5.883036881 Take the square root of each side: x = {-2.425497244, 2.425497244}Subproblem 2
x2 + -1.666666667 = -4.216370214 Simplifying x2 + -1.666666667 = -4.216370214 Reorder the terms: -1.666666667 + x2 = -4.216370214 Solving -1.666666667 + x2 = -4.216370214 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 = -4.216370214 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x2 = -4.216370214 + 1.666666667 x2 = -4.216370214 + 1.666666667 Combine like terms: -4.216370214 + 1.666666667 = -2.549703547 x2 = -2.549703547 Simplifying x2 = -2.549703547 Reorder the terms: 2.549703547 + x2 = -2.549703547 + 2.549703547 Combine like terms: -2.549703547 + 2.549703547 = 0.000000000 2.549703547 + 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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