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Simplifying -9x2 + -12x + 4 = 17 Reorder the terms: 4 + -12x + -9x2 = 17 Solving 4 + -12x + -9x2 = 17 Solving for variable 'x'. Reorder the terms: 4 + -17 + -12x + -9x2 = 17 + -17 Combine like terms: 4 + -17 = -13 -13 + -12x + -9x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -13 + -12x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 12x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying 13 + 12x + 9x2 = 0 Solving 13 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.444444444 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + 1.333333333x + -1.444444444 + x2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + 1.333333333x + x2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -1.444444444 1.333333333x + x2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 1.333333333x + x2 = -1.444444444 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 = -1.444444444 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -1.444444444 + 0.4444444442 Combine like terms: -1.444444444 + 0.4444444442 = -0.9999999998 0.4444444442 + 1.333333333x + x2 = -0.9999999998 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -0.9999999998 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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