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Simplifying 14d3 + -7d2 + d = 0 Reorder the terms: d + -7d2 + 14d3 = 0 Solving d + -7d2 + 14d3 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), 'd'. d(1 + -7d + 14d2) = 0Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(1 + -7d + 14d2)' equal to zero and attempt to solve: Simplifying 1 + -7d + 14d2 = 0 Solving 1 + -7d + 14d2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.07142857143 + -0.5d + d2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -0.5d + -0.07142857143 + d2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -0.5d + d2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -0.5d + d2 = 0 + -0.07142857143 -0.5d + d2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -0.5d + d2 = -0.07142857143 The d term is -0.5d. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5d + 0.0625 + d2 = -0.07142857143 + 0.0625 Reorder the terms: 0.0625 + -0.5d + d2 = -0.07142857143 + 0.0625 Combine like terms: -0.07142857143 + 0.0625 = -0.00892857143 0.0625 + -0.5d + d2 = -0.00892857143 Factor a perfect square on the left side: (d + -0.25)(d + -0.25) = -0.00892857143 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
d = {0}
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