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Simplifying 20x3 + 28x2 + 60x = 0 Reorder the terms: 60x + 28x2 + 20x3 = 0 Solving 60x + 28x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(15 + 7x + 5x2) = 0 Ignore the factor 4.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 '(15 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 15 + 7x + 5x2 = 0 Solving 15 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3 + 1.4x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.4x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 1.4x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.4x + x2 = 0 + -3 1.4x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.4x + x2 = -3 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -3 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -3 + 0.49 Combine like terms: -3 + 0.49 = -2.51 0.49 + 1.4x + x2 = -2.51 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -2.51 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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