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Simplifying -6x(x + -1) = 108 Reorder the terms: -6x(-1 + x) = 108 (-1 * -6x + x * -6x) = 108 (6x + -6x2) = 108 Solving 6x + -6x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + 6x + -6x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + 6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-18 + x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-18 + x + -1x2)' equal to zero and attempt to solve: Simplifying -18 + x + -1x2 = 0 Solving -18 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 18 + -1x + x2 = 0 Move the constant term to the right: Add '-18' to each side of the equation. 18 + -1x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -1x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x + x2 = 0 + -18 -1x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -1x + x2 = -18 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. -1x + 0.25 + x2 = -18 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -18 + 0.25 Combine like terms: -18 + 0.25 = -17.75 0.25 + -1x + x2 = -17.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -17.75 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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