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Simplifying -3x2 + -36x + -109 = 0 Reorder the terms: -109 + -36x + -3x2 = 0 Solving -109 + -36x + -3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(109 + 36x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(109 + 36x + 3x2)' equal to zero and attempt to solve: Simplifying 109 + 36x + 3x2 = 0 Solving 109 + 36x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 36.33333333 + 12x + x2 = 0 Move the constant term to the right: Add '-36.33333333' to each side of the equation. 36.33333333 + 12x + -36.33333333 + x2 = 0 + -36.33333333 Reorder the terms: 36.33333333 + -36.33333333 + 12x + x2 = 0 + -36.33333333 Combine like terms: 36.33333333 + -36.33333333 = 0.00000000 0.00000000 + 12x + x2 = 0 + -36.33333333 12x + x2 = 0 + -36.33333333 Combine like terms: 0 + -36.33333333 = -36.33333333 12x + x2 = -36.33333333 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = -36.33333333 + 36 Reorder the terms: 36 + 12x + x2 = -36.33333333 + 36 Combine like terms: -36.33333333 + 36 = -0.33333333 36 + 12x + x2 = -0.33333333 Factor a perfect square on the left side: (x + 6)(x + 6) = -0.33333333 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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