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Simplifying -2x3 + 180x2 + -4500x = 0 Reorder the terms: -4500x + 180x2 + -2x3 = 0 Solving -4500x + 180x2 + -2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-2250 + 90x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2250 + 90x + -1x2)' equal to zero and attempt to solve: Simplifying -2250 + 90x + -1x2 = 0 Solving -2250 + 90x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2250 + -90x + x2 = 0 Move the constant term to the right: Add '-2250' to each side of the equation. 2250 + -90x + -2250 + x2 = 0 + -2250 Reorder the terms: 2250 + -2250 + -90x + x2 = 0 + -2250 Combine like terms: 2250 + -2250 = 0 0 + -90x + x2 = 0 + -2250 -90x + x2 = 0 + -2250 Combine like terms: 0 + -2250 = -2250 -90x + x2 = -2250 The x term is -90x. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90x + 2025 + x2 = -2250 + 2025 Reorder the terms: 2025 + -90x + x2 = -2250 + 2025 Combine like terms: -2250 + 2025 = -225 2025 + -90x + x2 = -225 Factor a perfect square on the left side: (x + -45)(x + -45) = -225 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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