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Simplifying -5x + -2x(x + 2) = 81 Reorder the terms: -5x + -2x(2 + x) = 81 -5x + (2 * -2x + x * -2x) = 81 -5x + (-4x + -2x2) = 81 Combine like terms: -5x + -4x = -9x -9x + -2x2 = 81 Solving -9x + -2x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + -9x + -2x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + -9x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(81 + 9x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(81 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying 81 + 9x + 2x2 = 0 Solving 81 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 40.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '-40.5' to each side of the equation. 40.5 + 4.5x + -40.5 + x2 = 0 + -40.5 Reorder the terms: 40.5 + -40.5 + 4.5x + x2 = 0 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + 4.5x + x2 = 0 + -40.5 4.5x + x2 = 0 + -40.5 Combine like terms: 0 + -40.5 = -40.5 4.5x + x2 = -40.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = -40.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = -40.5 + 5.0625 Combine like terms: -40.5 + 5.0625 = -35.4375 5.0625 + 4.5x + x2 = -35.4375 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = -35.4375 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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