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Simplifying 0 = 2x2 + 30 + 3x2 + 4x2 + 14 + x Reorder the terms: 0 = 30 + 14 + x + 2x2 + 3x2 + 4x2 Combine like terms: 30 + 14 = 44 0 = 44 + x + 2x2 + 3x2 + 4x2 Combine like terms: 2x2 + 3x2 = 5x2 0 = 44 + x + 5x2 + 4x2 Combine like terms: 5x2 + 4x2 = 9x2 0 = 44 + x + 9x2 Solving 0 = 44 + x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -44 = -44 -44 + -1x + -9x2 = 44 + x + 9x2 + -44 + -1x + -9x2 Reorder the terms: -44 + -1x + -9x2 = 44 + -44 + x + -1x + 9x2 + -9x2 Combine like terms: 44 + -44 = 0 -44 + -1x + -9x2 = 0 + x + -1x + 9x2 + -9x2 -44 + -1x + -9x2 = x + -1x + 9x2 + -9x2 Combine like terms: x + -1x = 0 -44 + -1x + -9x2 = 0 + 9x2 + -9x2 -44 + -1x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -44 + -1x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(44 + x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(44 + x + 9x2)' equal to zero and attempt to solve: Simplifying 44 + x + 9x2 = 0 Solving 44 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.888888889 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-4.888888889' to each side of the equation. 4.888888889 + 0.1111111111x + -4.888888889 + x2 = 0 + -4.888888889 Reorder the terms: 4.888888889 + -4.888888889 + 0.1111111111x + x2 = 0 + -4.888888889 Combine like terms: 4.888888889 + -4.888888889 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + -4.888888889 0.1111111111x + x2 = 0 + -4.888888889 Combine like terms: 0 + -4.888888889 = -4.888888889 0.1111111111x + x2 = -4.888888889 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = -4.888888889 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -4.888888889 + 0.25 Combine like terms: -4.888888889 + 0.25 = -4.638888889 0.25 + 0.1111111111x + x2 = -4.638888889 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.638888889 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. The solution to this equation could not be determined.
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