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Simplifying 12x2 + -76x + 374 = 0 Reorder the terms: 374 + -76x + 12x2 = 0 Solving 374 + -76x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(187 + -38x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(187 + -38x + 6x2)' equal to zero and attempt to solve: Simplifying 187 + -38x + 6x2 = 0 Solving 187 + -38x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 31.16666667 + -6.333333333x + x2 = 0 Move the constant term to the right: Add '-31.16666667' to each side of the equation. 31.16666667 + -6.333333333x + -31.16666667 + x2 = 0 + -31.16666667 Reorder the terms: 31.16666667 + -31.16666667 + -6.333333333x + x2 = 0 + -31.16666667 Combine like terms: 31.16666667 + -31.16666667 = 0.00000000 0.00000000 + -6.333333333x + x2 = 0 + -31.16666667 -6.333333333x + x2 = 0 + -31.16666667 Combine like terms: 0 + -31.16666667 = -31.16666667 -6.333333333x + x2 = -31.16666667 The x term is -6.333333333x. Take half its coefficient (-3.166666667). Square it (10.02777778) and add it to both sides. Add '10.02777778' to each side of the equation. -6.333333333x + 10.02777778 + x2 = -31.16666667 + 10.02777778 Reorder the terms: 10.02777778 + -6.333333333x + x2 = -31.16666667 + 10.02777778 Combine like terms: -31.16666667 + 10.02777778 = -21.13888889 10.02777778 + -6.333333333x + x2 = -21.13888889 Factor a perfect square on the left side: (x + -3.166666667)(x + -3.166666667) = -21.13888889 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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