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Simplifying 6x4 + 8x3 = -26x2 Reorder the terms: 8x3 + 6x4 = -26x2 Solving 8x3 + 6x4 = -26x2 Solving for variable 'x'. Reorder the terms: 26x2 + 8x3 + 6x4 = -26x2 + 26x2 Combine like terms: -26x2 + 26x2 = 0 26x2 + 8x3 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(13 + 4x + 3x2) = 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 '(13 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 13 + 4x + 3x2 = 0 Solving 13 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-4.333333333' to each side of the equation. 4.333333333 + 1.333333333x + -4.333333333 + x2 = 0 + -4.333333333 Reorder the terms: 4.333333333 + -4.333333333 + 1.333333333x + x2 = 0 + -4.333333333 Combine like terms: 4.333333333 + -4.333333333 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -4.333333333 1.333333333x + x2 = 0 + -4.333333333 Combine like terms: 0 + -4.333333333 = -4.333333333 1.333333333x + x2 = -4.333333333 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -4.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -4.333333333 + 0.4444444442 Combine like terms: -4.333333333 + 0.4444444442 = -3.8888888888 0.4444444442 + 1.333333333x + x2 = -3.8888888888 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -3.8888888888 Can't calculate square root of the right side. 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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