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Simplifying 14x3 + 6x2 + 6x = 0 Reorder the terms: 6x + 6x2 + 14x3 = 0 Solving 6x + 6x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + 3x + 7x2) = 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 '(3 + 3x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + 7x2 = 0 Solving 3 + 3x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 0.4285714286x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 0.4285714286x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 0.4285714286x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 0.4285714286x + x2 = 0 + -0.4285714286 0.4285714286x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 0.4285714286x + x2 = -0.4285714286 The x term is 0.4285714286x. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x + 0.04591836735 + x2 = -0.4285714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x + x2 = -0.4285714286 + 0.04591836735 Combine like terms: -0.4285714286 + 0.04591836735 = -0.38265306125 0.04591836735 + 0.4285714286x + x2 = -0.38265306125 Factor a perfect square on the left side: (x + 0.2142857143)(x + 0.2142857143) = -0.38265306125 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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