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Simplifying -3x2 = 4x + 9 Reorder the terms: -3x2 = 9 + 4x Solving -3x2 = 9 + 4x Solving for variable 'x'. Reorder the terms: -9 + -4x + -3x2 = 9 + 4x + -9 + -4x Reorder the terms: -9 + -4x + -3x2 = 9 + -9 + 4x + -4x Combine like terms: 9 + -9 = 0 -9 + -4x + -3x2 = 0 + 4x + -4x -9 + -4x + -3x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -9 + -4x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 4x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 9 + 4x + 3x2 = 0 Solving 9 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.333333333x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 1.333333333x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.333333333x + x2 = 0 + -3 1.333333333x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.333333333x + x2 = -3 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 = -3 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -3 + 0.4444444442 Combine like terms: -3 + 0.4444444442 = -2.5555555558 0.4444444442 + 1.333333333x + x2 = -2.5555555558 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -2.5555555558 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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