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Simplifying -27x2 + -36x + -63 = 0 Reorder the terms: -63 + -36x + -27x2 = 0 Solving -63 + -36x + -27x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-9'. -9(7 + 4x + 3x2) = 0 Ignore the factor -9.Subproblem 1
Set the factor '(7 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 3x2 = 0 Solving 7 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 1.333333333x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 1.333333333x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -2.333333333 1.333333333x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 1.333333333x + x2 = -2.333333333 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = -2.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -2.333333333 + 0.4444444442 Combine like terms: -2.333333333 + 0.4444444442 = -1.8888888888 0.4444444442 + 1.333333333x + x2 = -1.8888888888 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.8888888888 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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