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Simplifying 24x2 + 14x + 108 = 0 Reorder the terms: 108 + 14x + 24x2 = 0 Solving 108 + 14x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(54 + 7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(54 + 7x + 12x2)' equal to zero and attempt to solve: Simplifying 54 + 7x + 12x2 = 0 Solving 54 + 7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 4.5 + 0.5833333333x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 0.5833333333x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 0.5833333333x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 0.5833333333x + x2 = 0 + -4.5 0.5833333333x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 0.5833333333x + x2 = -4.5 The x term is 0.5833333333x. Take half its coefficient (0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. 0.5833333333x + 0.08506944446 + x2 = -4.5 + 0.08506944446 Reorder the terms: 0.08506944446 + 0.5833333333x + x2 = -4.5 + 0.08506944446 Combine like terms: -4.5 + 0.08506944446 = -4.41493055554 0.08506944446 + 0.5833333333x + x2 = -4.41493055554 Factor a perfect square on the left side: (x + 0.2916666667)(x + 0.2916666667) = -4.41493055554 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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