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Simplifying -19x3 + -12x2 + -16x = 0 Reorder the terms: -16x + -12x2 + -19x3 = 0 Solving -16x + -12x2 + -19x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1x'. -1x(16 + 12x + 19x2) = 0 Ignore the factor -1.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 '(16 + 12x + 19x2)' equal to zero and attempt to solve: Simplifying 16 + 12x + 19x2 = 0 Solving 16 + 12x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. 0.8421052632 + 0.6315789474x + x2 = 0 Move the constant term to the right: Add '-0.8421052632' to each side of the equation. 0.8421052632 + 0.6315789474x + -0.8421052632 + x2 = 0 + -0.8421052632 Reorder the terms: 0.8421052632 + -0.8421052632 + 0.6315789474x + x2 = 0 + -0.8421052632 Combine like terms: 0.8421052632 + -0.8421052632 = 0.0000000000 0.0000000000 + 0.6315789474x + x2 = 0 + -0.8421052632 0.6315789474x + x2 = 0 + -0.8421052632 Combine like terms: 0 + -0.8421052632 = -0.8421052632 0.6315789474x + x2 = -0.8421052632 The x term is 0.6315789474x. Take half its coefficient (0.3157894737). Square it (0.09972299170) and add it to both sides. Add '0.09972299170' to each side of the equation. 0.6315789474x + 0.09972299170 + x2 = -0.8421052632 + 0.09972299170 Reorder the terms: 0.09972299170 + 0.6315789474x + x2 = -0.8421052632 + 0.09972299170 Combine like terms: -0.8421052632 + 0.09972299170 = -0.7423822715 0.09972299170 + 0.6315789474x + x2 = -0.7423822715 Factor a perfect square on the left side: (x + 0.3157894737)(x + 0.3157894737) = -0.7423822715 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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