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Simplifying 3x3(2x3 + -10x) + -4x2(x2 + 1) = 0 Reorder the terms: 3x3(-10x + 2x3) + -4x2(x2 + 1) = 0 (-10x * 3x3 + 2x3 * 3x3) + -4x2(x2 + 1) = 0 (-30x4 + 6x6) + -4x2(x2 + 1) = 0 Reorder the terms: -30x4 + 6x6 + -4x2(1 + x2) = 0 -30x4 + 6x6 + (1 * -4x2 + x2 * -4x2) = 0 -30x4 + 6x6 + (-4x2 + -4x4) = 0 Reorder the terms: -4x2 + -30x4 + -4x4 + 6x6 = 0 Combine like terms: -30x4 + -4x4 = -34x4 -4x2 + -34x4 + 6x6 = 0 Solving -4x2 + -34x4 + 6x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-2 + -17x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-2 + -17x2 + 3x4)' equal to zero and attempt to solve: Simplifying -2 + -17x2 + 3x4 = 0 Solving -2 + -17x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -5.666666667x2 + x4 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -5.666666667x2 + 0.6666666667 + x4 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -5.666666667x2 + x4 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -5.666666667x2 + x4 = 0 + 0.6666666667 -5.666666667x2 + x4 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -5.666666667x2 + x4 = 0.6666666667 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 = 0.6666666667 + 8.027777782 Reorder the terms: 8.027777782 + -5.666666667x2 + x4 = 0.6666666667 + 8.027777782 Combine like terms: 0.6666666667 + 8.027777782 = 8.6944444487 8.027777782 + -5.666666667x2 + x4 = 8.6944444487 Factor a perfect square on the left side: (x2 + -2.833333334)(x2 + -2.833333334) = 8.6944444487 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (x2 + -2.833333334) equal to 2.948634336 and -2.948634336.Subproblem 1
x2 + -2.833333334 = 2.948634336 Simplifying x2 + -2.833333334 = 2.948634336 Reorder the terms: -2.833333334 + x2 = 2.948634336 Solving -2.833333334 + x2 = 2.948634336 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 = 2.948634336 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x2 = 2.948634336 + 2.833333334 x2 = 2.948634336 + 2.833333334 Combine like terms: 2.948634336 + 2.833333334 = 5.78196767 x2 = 5.78196767 Simplifying x2 = 5.78196767 Take the square root of each side: x = {-2.404572243, 2.404572243}Subproblem 2
x2 + -2.833333334 = -2.948634336 Simplifying x2 + -2.833333334 = -2.948634336 Reorder the terms: -2.833333334 + x2 = -2.948634336 Solving -2.833333334 + x2 = -2.948634336 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 = -2.948634336 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x2 = -2.948634336 + 2.833333334 x2 = -2.948634336 + 2.833333334 Combine like terms: -2.948634336 + 2.833333334 = -0.115301002 x2 = -0.115301002 Simplifying x2 = -0.115301002 Reorder the terms: 0.115301002 + x2 = -0.115301002 + 0.115301002 Combine like terms: -0.115301002 + 0.115301002 = 0.000000000 0.115301002 + 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. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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