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Simplifying 14x3 + 10x2 + 4x = 0 Reorder the terms: 4x + 10x2 + 14x3 = 0 Solving 4x + 10x2 + 14x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(2 + 5x + 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 '(2 + 5x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + 7x2 = 0 Solving 2 + 5x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 0.7142857143x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.7142857143x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.7142857143x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.7142857143x + x2 = 0 + -0.2857142857 0.7142857143x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.7142857143x + x2 = -0.2857142857 The x term is 0.7142857143x. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x + 0.1275510204 + x2 = -0.2857142857 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x + x2 = -0.2857142857 + 0.1275510204 Combine like terms: -0.2857142857 + 0.1275510204 = -0.1581632653 0.1275510204 + 0.7142857143x + x2 = -0.1581632653 Factor a perfect square on the left side: (x + 0.3571428572)(x + 0.3571428572) = -0.1581632653 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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