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Simplifying 2x(4 + -7x) + -1x(4x + 5) = 4x + 81 (4 * 2x + -7x * 2x) + -1x(4x + 5) = 4x + 81 (8x + -14x2) + -1x(4x + 5) = 4x + 81 Reorder the terms: 8x + -14x2 + -1x(5 + 4x) = 4x + 81 8x + -14x2 + (5 * -1x + 4x * -1x) = 4x + 81 8x + -14x2 + (-5x + -4x2) = 4x + 81 Reorder the terms: 8x + -5x + -14x2 + -4x2 = 4x + 81 Combine like terms: 8x + -5x = 3x 3x + -14x2 + -4x2 = 4x + 81 Combine like terms: -14x2 + -4x2 = -18x2 3x + -18x2 = 4x + 81 Reorder the terms: 3x + -18x2 = 81 + 4x Solving 3x + -18x2 = 81 + 4x Solving for variable 'x'. Reorder the terms: -81 + 3x + -4x + -18x2 = 81 + 4x + -81 + -4x Combine like terms: 3x + -4x = -1x -81 + -1x + -18x2 = 81 + 4x + -81 + -4x Reorder the terms: -81 + -1x + -18x2 = 81 + -81 + 4x + -4x Combine like terms: 81 + -81 = 0 -81 + -1x + -18x2 = 0 + 4x + -4x -81 + -1x + -18x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -81 + -1x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(81 + x + 18x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(81 + x + 18x2)' equal to zero and attempt to solve: Simplifying 81 + x + 18x2 = 0 Solving 81 + x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 4.5 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 0.05555555556x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 0.05555555556x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 0.05555555556x + x2 = 0 + -4.5 0.05555555556x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 0.05555555556x + x2 = -4.5 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. 0.05555555556x + 0.25 + x2 = -4.5 + 0.25 Reorder the terms: 0.25 + 0.05555555556x + x2 = -4.5 + 0.25 Combine like terms: -4.5 + 0.25 = -4.25 0.25 + 0.05555555556x + x2 = -4.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.25 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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