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Simplifying 5x4 + -30x3 + 180x2 = 0 Reorder the terms: 180x2 + -30x3 + 5x4 = 0 Solving 180x2 + -30x3 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x2'. 5x2(36 + -6x + x2) = 0 Ignore the factor 5.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 '(36 + -6x + x2)' equal to zero and attempt to solve: Simplifying 36 + -6x + x2 = 0 Solving 36 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -6x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -6x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -6x + x2 = 0 + -36 -6x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -6x + x2 = -36 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -36 + 9 Reorder the terms: 9 + -6x + x2 = -36 + 9 Combine like terms: -36 + 9 = -27 9 + -6x + x2 = -27 Factor a perfect square on the left side: (x + -3)(x + -3) = -27 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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