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Simplifying -36x2 + -18x + 6 = 27 Reorder the terms: 6 + -18x + -36x2 = 27 Solving 6 + -18x + -36x2 = 27 Solving for variable 'x'. Reorder the terms: 6 + -27 + -18x + -36x2 = 27 + -27 Combine like terms: 6 + -27 = -21 -21 + -18x + -36x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -21 + -18x + -36x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(7 + 6x + 12x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(7 + 6x + 12x2)' equal to zero and attempt to solve: Simplifying 7 + 6x + 12x2 = 0 Solving 7 + 6x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 0.5x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 0.5x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + -0.5833333333 0.5x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 0.5x + x2 = -0.5833333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.5833333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.5833333333 + 0.0625 Combine like terms: -0.5833333333 + 0.0625 = -0.5208333333 0.0625 + 0.5x + x2 = -0.5208333333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.5208333333 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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