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Simplifying (3x + 4x2 + 7x3) = 0 Remove parenthesis around (3x + 4x2 + 7x3) 3x + 4x2 + 7x3 = 0 Solving 3x + 4x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 4x + 7x2) = 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 '(3 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 7x2 = 0 Solving 3 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 0.5714285714x + -0.4285714286 + x2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 0.5714285714x + x2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + -0.4285714286 0.5714285714x + x2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 0.5714285714x + x2 = -0.4285714286 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = -0.4285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -0.4285714286 + 0.08163265305 Combine like terms: -0.4285714286 + 0.08163265305 = -0.34693877555 0.08163265305 + 0.5714285714x + x2 = -0.34693877555 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = -0.34693877555 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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