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Simplifying 0 = 3x2 + 4x + 16 Reorder the terms: 0 = 16 + 4x + 3x2 Solving 0 = 16 + 4x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -4x + -3x2 = 16 + 4x + 3x2 + -16 + -4x + -3x2 Reorder the terms: -16 + -4x + -3x2 = 16 + -16 + 4x + -4x + 3x2 + -3x2 Combine like terms: 16 + -16 = 0 -16 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2 -16 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 -16 + -4x + -3x2 = 0 + 3x2 + -3x2 -16 + -4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -16 + -4x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 4x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 16 + 4x + 3x2 = 0 Solving 16 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 1.333333333x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 1.333333333x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + -5.333333333 1.333333333x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 1.333333333x + x2 = -5.333333333 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 = -5.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -5.333333333 + 0.4444444442 Combine like terms: -5.333333333 + 0.4444444442 = -4.8888888888 0.4444444442 + 1.333333333x + x2 = -4.8888888888 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -4.8888888888 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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