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Simplifying 9x2 = 12x + -84 Reorder the terms: 9x2 = -84 + 12x Solving 9x2 = -84 + 12x Solving for variable 'x'. Reorder the terms: 84 + -12x + 9x2 = -84 + 12x + 84 + -12x Reorder the terms: 84 + -12x + 9x2 = -84 + 84 + 12x + -12x Combine like terms: -84 + 84 = 0 84 + -12x + 9x2 = 0 + 12x + -12x 84 + -12x + 9x2 = 12x + -12x Combine like terms: 12x + -12x = 0 84 + -12x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(28 + -4x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(28 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying 28 + -4x + 3x2 = 0 Solving 28 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -1.333333333x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -1.333333333x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -9.333333333 -1.333333333x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -1.333333333x + x2 = -9.333333333 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 = -9.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -9.333333333 + 0.4444444442 Combine like terms: -9.333333333 + 0.4444444442 = -8.8888888888 0.4444444442 + -1.333333333x + x2 = -8.8888888888 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -8.8888888888 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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