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Simplifying 3x4 + -11x2 + -16 = 0 Reorder the terms: -16 + -11x2 + 3x4 = 0 Solving -16 + -11x2 + 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'. -5.333333333 + -3.666666667x2 + x4 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -3.666666667x2 + 5.333333333 + x4 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -3.666666667x2 + x4 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -3.666666667x2 + x4 = 0 + 5.333333333 -3.666666667x2 + x4 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -3.666666667x2 + x4 = 5.333333333 The x term is -3.666666667x2. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x2 + 3.361111114 + x4 = 5.333333333 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x2 + x4 = 5.333333333 + 3.361111114 Combine like terms: 5.333333333 + 3.361111114 = 8.694444447 3.361111114 + -3.666666667x2 + x4 = 8.694444447 Factor a perfect square on the left side: (x2 + -1.833333334)(x2 + -1.833333334) = 8.694444447 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (x2 + -1.833333334) equal to 2.948634336 and -2.948634336.Subproblem 1
x2 + -1.833333334 = 2.948634336 Simplifying x2 + -1.833333334 = 2.948634336 Reorder the terms: -1.833333334 + x2 = 2.948634336 Solving -1.833333334 + x2 = 2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x2 = 2.948634336 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x2 = 2.948634336 + 1.833333334 x2 = 2.948634336 + 1.833333334 Combine like terms: 2.948634336 + 1.833333334 = 4.78196767 x2 = 4.78196767 Simplifying x2 = 4.78196767 Take the square root of each side: x = {-2.18677106, 2.18677106}Subproblem 2
x2 + -1.833333334 = -2.948634336 Simplifying x2 + -1.833333334 = -2.948634336 Reorder the terms: -1.833333334 + x2 = -2.948634336 Solving -1.833333334 + x2 = -2.948634336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x2 = -2.948634336 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x2 = -2.948634336 + 1.833333334 x2 = -2.948634336 + 1.833333334 Combine like terms: -2.948634336 + 1.833333334 = -1.115301002 x2 = -1.115301002 Simplifying x2 = -1.115301002 Reorder the terms: 1.115301002 + x2 = -1.115301002 + 1.115301002 Combine like terms: -1.115301002 + 1.115301002 = 0.000000000 1.115301002 + 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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