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Simplifying 5x = (9x2) + 16 + 24x Reorder the terms: 5x = 16 + 24x + (9x2) Solving 5x = 16 + 24x + (9x2) Solving for variable 'x'. Reorder the terms: -16 + 5x + -24x + (-9x2) = 16 + 24x + (9x2) + -16 + -24x + (-9x2) Combine like terms: 5x + -24x = -19x -16 + -19x + (-9x2) = 16 + 24x + (9x2) + -16 + -24x + (-9x2) Reorder the terms: -16 + -19x + (-9x2) = 16 + -16 + 24x + -24x + (9x2) + (-9x2) Combine like terms: 16 + -16 = 0 -16 + -19x + (-9x2) = 0 + 24x + -24x + (9x2) + (-9x2) -16 + -19x + (-9x2) = 24x + -24x + (9x2) + (-9x2) Combine like terms: 24x + -24x = 0 -16 + -19x + (-9x2) = 0 + (9x2) + (-9x2) -16 + -19x + (-9x2) = (9x2) + (-9x2) Combine like terms: (9x2) + (-9x2) = 0 -16 + -19x + (-9x2) = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 19x + (9x2)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 19x + (9x2))' equal to zero and attempt to solve: Simplifying 16 + 19x + (9x2) = 0 Solving 16 + 19x + (9x2) = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.777777778 + 2.111111111x + x2 = 0 Move the constant term to the right: Add '-1.777777778' to each side of the equation. 1.777777778 + 2.111111111x + -1.777777778 + x2 = 0 + -1.777777778 Reorder the terms: 1.777777778 + -1.777777778 + 2.111111111x + x2 = 0 + -1.777777778 Combine like terms: 1.777777778 + -1.777777778 = 0.000000000 0.000000000 + 2.111111111x + x2 = 0 + -1.777777778 2.111111111x + x2 = 0 + -1.777777778 Combine like terms: 0 + -1.777777778 = -1.777777778 2.111111111x + x2 = -1.777777778 The x term is 2.111111111x. Take half its coefficient (1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. 2.111111111x + 1.114197532 + x2 = -1.777777778 + 1.114197532 Reorder the terms: 1.114197532 + 2.111111111x + x2 = -1.777777778 + 1.114197532 Combine like terms: -1.777777778 + 1.114197532 = -0.663580246 1.114197532 + 2.111111111x + x2 = -0.663580246 Factor a perfect square on the left side: ((x) + 1.055555556)((x) + 1.055555556) = -0.663580246 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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