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Simplifying 4x4 + -1x3 + 20x2 = 0 Reorder the terms: 20x2 + -1x3 + 4x4 = 0 Solving 20x2 + -1x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(20 + -1x + 4x2) = 0Subproblem 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 '(20 + -1x + 4x2)' equal to zero and attempt to solve: Simplifying 20 + -1x + 4x2 = 0 Solving 20 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -0.25x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -0.25x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -0.25x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -0.25x + x2 = 0 + -5 -0.25x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -0.25x + x2 = -5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = -5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = -5 + 0.015625 Combine like terms: -5 + 0.015625 = -4.984375 0.015625 + -0.25x + x2 = -4.984375 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = -4.984375 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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