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Simplifying 4x + 7x2 + 3x + 9x3 + -4x2 = 0 Reorder the terms: 4x + 3x + 7x2 + -4x2 + 9x3 = 0 Combine like terms: 4x + 3x = 7x 7x + 7x2 + -4x2 + 9x3 = 0 Combine like terms: 7x2 + -4x2 = 3x2 7x + 3x2 + 9x3 = 0 Solving 7x + 3x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 3x + 9x2) = 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 '(7 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying 7 + 3x + 9x2 = 0 Solving 7 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 0.3333333333x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 0.3333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + -0.7777777778 0.3333333333x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 0.3333333333x + x2 = -0.7777777778 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.7777777778 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.7777777778 + 0.02777777779 Combine like terms: -0.7777777778 + 0.02777777779 = -0.75000000001 0.02777777779 + 0.3333333333x + x2 = -0.75000000001 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.75000000001 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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