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Simplifying 90x3 + -28x2 + 12x = 0 Reorder the terms: 12x + -28x2 + 90x3 = 0 Solving 12x + -28x2 + 90x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(6 + -14x + 45x2) = 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 '(6 + -14x + 45x2)' equal to zero and attempt to solve: Simplifying 6 + -14x + 45x2 = 0 Solving 6 + -14x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. 0.1333333333 + -0.3111111111x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + -0.3111111111x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + -0.3111111111x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + -0.3111111111x + x2 = 0 + -0.1333333333 -0.3111111111x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 -0.3111111111x + x2 = -0.1333333333 The x term is -0.3111111111x. Take half its coefficient (-0.1555555556). Square it (0.02419753088) and add it to both sides. Add '0.02419753088' to each side of the equation. -0.3111111111x + 0.02419753088 + x2 = -0.1333333333 + 0.02419753088 Reorder the terms: 0.02419753088 + -0.3111111111x + x2 = -0.1333333333 + 0.02419753088 Combine like terms: -0.1333333333 + 0.02419753088 = -0.10913580242 0.02419753088 + -0.3111111111x + x2 = -0.10913580242 Factor a perfect square on the left side: (x + -0.1555555556)(x + -0.1555555556) = -0.10913580242 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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