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Simplifying 6x2 + 8x + 294 = 0 Reorder the terms: 294 + 8x + 6x2 = 0 Solving 294 + 8x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(147 + 4x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(147 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying 147 + 4x + 3x2 = 0 Solving 147 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 49 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-49' to each side of the equation. 49 + 1.333333333x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + 1.333333333x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 1.333333333x + x2 = 0 + -49 1.333333333x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 1.333333333x + x2 = -49 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 = -49 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -49 + 0.4444444442 Combine like terms: -49 + 0.4444444442 = -48.5555555558 0.4444444442 + 1.333333333x + x2 = -48.5555555558 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = -48.5555555558 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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