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Simplifying 0 = 9x2 + 12x + 20 Reorder the terms: 0 = 20 + 12x + 9x2 Solving 0 = 20 + 12x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -12x + -9x2 = 20 + 12x + 9x2 + -20 + -12x + -9x2 Reorder the terms: -20 + -12x + -9x2 = 20 + -20 + 12x + -12x + 9x2 + -9x2 Combine like terms: 20 + -20 = 0 -20 + -12x + -9x2 = 0 + 12x + -12x + 9x2 + -9x2 -20 + -12x + -9x2 = 12x + -12x + 9x2 + -9x2 Combine like terms: 12x + -12x = 0 -20 + -12x + -9x2 = 0 + 9x2 + -9x2 -20 + -12x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -20 + -12x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 12x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 12x + 9x2)' equal to zero and attempt to solve: Simplifying 20 + 12x + 9x2 = 0 Solving 20 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2.222222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-2.222222222' to each side of the equation. 2.222222222 + 1.333333333x + -2.222222222 + x2 = 0 + -2.222222222 Reorder the terms: 2.222222222 + -2.222222222 + 1.333333333x + x2 = 0 + -2.222222222 Combine like terms: 2.222222222 + -2.222222222 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -2.222222222 1.333333333x + x2 = 0 + -2.222222222 Combine like terms: 0 + -2.222222222 = -2.222222222 1.333333333x + x2 = -2.222222222 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 = -2.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -2.222222222 + 0.4444444442 Combine like terms: -2.222222222 + 0.4444444442 = -1.7777777778 0.4444444442 + 1.333333333x + x2 = -1.7777777778 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -1.7777777778 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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