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Simplifying 6x3 + 17x2 + 15x = 0 Reorder the terms: 15x + 17x2 + 6x3 = 0 Solving 15x + 17x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(15 + 17x + 6x2) = 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 '(15 + 17x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + 17x + 6x2 = 0 Solving 15 + 17x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + 2.833333333x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2.833333333x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2.833333333x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2.833333333x + x2 = 0 + -2.5 2.833333333x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2.833333333x + x2 = -2.5 The x term is 2.833333333x. Take half its coefficient (1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. 2.833333333x + 2.006944445 + x2 = -2.5 + 2.006944445 Reorder the terms: 2.006944445 + 2.833333333x + x2 = -2.5 + 2.006944445 Combine like terms: -2.5 + 2.006944445 = -0.493055555 2.006944445 + 2.833333333x + x2 = -0.493055555 Factor a perfect square on the left side: (x + 1.416666667)(x + 1.416666667) = -0.493055555 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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