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Simplifying 8x3 + 28x2 + 104x = 0 Reorder the terms: 104x + 28x2 + 8x3 = 0 Solving 104x + 28x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(26 + 7x + 2x2) = 0 Ignore the factor 4.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 '(26 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 26 + 7x + 2x2 = 0 Solving 26 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13 + 3.5x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + 3.5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 3.5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3.5x + x2 = 0 + -13 3.5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 3.5x + x2 = -13 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -13 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -13 + 3.0625 Combine like terms: -13 + 3.0625 = -9.9375 3.0625 + 3.5x + x2 = -9.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -9.9375 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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