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Simplifying -3x4 + -17x2 + 81 = 0 Reorder the terms: 81 + -17x2 + -3x4 = 0 Solving 81 + -17x2 + -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'. -27 + 5.666666667x2 + x4 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 5.666666667x2 + 27 + x4 = 0 + 27 Reorder the terms: -27 + 27 + 5.666666667x2 + x4 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 5.666666667x2 + x4 = 0 + 27 5.666666667x2 + x4 = 0 + 27 Combine like terms: 0 + 27 = 27 5.666666667x2 + x4 = 27 The x term is 5.666666667x2. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x2 + 8.027777782 + x4 = 27 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x2 + x4 = 27 + 8.027777782 Combine like terms: 27 + 8.027777782 = 35.027777782 8.027777782 + 5.666666667x2 + x4 = 35.027777782 Factor a perfect square on the left side: (x2 + 2.833333334)(x2 + 2.833333334) = 35.027777782 Calculate the square root of the right side: 5.918426969 Break this problem into two subproblems by setting (x2 + 2.833333334) equal to 5.918426969 and -5.918426969.Subproblem 1
x2 + 2.833333334 = 5.918426969 Simplifying x2 + 2.833333334 = 5.918426969 Reorder the terms: 2.833333334 + x2 = 5.918426969 Solving 2.833333334 + x2 = 5.918426969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x2 = 5.918426969 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x2 = 5.918426969 + -2.833333334 x2 = 5.918426969 + -2.833333334 Combine like terms: 5.918426969 + -2.833333334 = 3.085093635 x2 = 3.085093635 Simplifying x2 = 3.085093635 Take the square root of each side: x = {-1.756443462, 1.756443462}Subproblem 2
x2 + 2.833333334 = -5.918426969 Simplifying x2 + 2.833333334 = -5.918426969 Reorder the terms: 2.833333334 + x2 = -5.918426969 Solving 2.833333334 + x2 = -5.918426969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x2 = -5.918426969 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x2 = -5.918426969 + -2.833333334 x2 = -5.918426969 + -2.833333334 Combine like terms: -5.918426969 + -2.833333334 = -8.751760303 x2 = -8.751760303 Simplifying x2 = -8.751760303 Reorder the terms: 8.751760303 + x2 = -8.751760303 + 8.751760303 Combine like terms: -8.751760303 + 8.751760303 = 0.000000000 8.751760303 + 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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