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Simplifying 0 = 6x2 + 20x4 + -4x3 Reorder the terms: 0 = 6x2 + -4x3 + 20x4 Solving 0 = 6x2 + -4x3 + 20x4 Solving for variable 'x'. Remove the zero: -6x2 + 4x3 + -20x4 = 6x2 + -4x3 + 20x4 + -6x2 + 4x3 + -20x4 Reorder the terms: -6x2 + 4x3 + -20x4 = 6x2 + -6x2 + -4x3 + 4x3 + 20x4 + -20x4 Combine like terms: 6x2 + -6x2 = 0 -6x2 + 4x3 + -20x4 = 0 + -4x3 + 4x3 + 20x4 + -20x4 -6x2 + 4x3 + -20x4 = -4x3 + 4x3 + 20x4 + -20x4 Combine like terms: -4x3 + 4x3 = 0 -6x2 + 4x3 + -20x4 = 0 + 20x4 + -20x4 -6x2 + 4x3 + -20x4 = 20x4 + -20x4 Combine like terms: 20x4 + -20x4 = 0 -6x2 + 4x3 + -20x4 = 0 Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-3 + 2x + -10x2) = 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 '(-3 + 2x + -10x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + -10x2 = 0 Solving -3 + 2x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. 0.3 + -0.2x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + -0.2x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + -0.2x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + -0.2x + x2 = 0.0 + -0.3 -0.2x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 -0.2x + x2 = -0.3 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.3 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.3 + 0.01 Combine like terms: -0.3 + 0.01 = -0.29 0.01 + -0.2x + x2 = -0.29 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -0.29 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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