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Simplifying (3x3) + (24x2) + (61x) = 0 Reorder the terms: (61x) + (24x2) + (3x3) = 0 Solving (61x) + (24x2) + (3x3) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(61 + (24x) + (3x2)) = 0Subproblem 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 '(61 + (24x) + (3x2))' equal to zero and attempt to solve: Simplifying 61 + (24x) + (3x2) = 0 Solving 61 + (24x) + (3x2) = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 20.33333333 + (8x) + x2 = 0 Move the constant term to the right: Add '-20.33333333' to each side of the equation. 20.33333333 + (8x) + -20.33333333 + x2 = 0 + -20.33333333 Reorder the terms: 20.33333333 + -20.33333333 + (8x) + x2 = 0 + -20.33333333 Combine like terms: 20.33333333 + -20.33333333 = 0.00000000 0.00000000 + (8x) + x2 = 0 + -20.33333333 (8x) + x2 = 0 + -20.33333333 Combine like terms: 0 + -20.33333333 = -20.33333333 (8x) + x2 = -20.33333333 The x term is (8x). Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. (8x) + 16 + x2 = -20.33333333 + 16 Reorder the terms: 16 + (8x) + x2 = -20.33333333 + 16 Combine like terms: -20.33333333 + 16 = -4.33333333 16 + (8x) + x2 = -4.33333333 Factor a perfect square on the left side: ((x) + 4)((x) + 4) = -4.33333333 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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