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Simplifying 6x2 + 38x + 144 = 0 Reorder the terms: 144 + 38x + 6x2 = 0 Solving 144 + 38x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(72 + 19x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + 19x + 3x2)' equal to zero and attempt to solve: Simplifying 72 + 19x + 3x2 = 0 Solving 72 + 19x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 24 + 6.333333333x + x2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + 6.333333333x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 6.333333333x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 6.333333333x + x2 = 0 + -24 6.333333333x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 6.333333333x + x2 = -24 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 = -24 + 10.02777778 Reorder the terms: 10.02777778 + 6.333333333x + x2 = -24 + 10.02777778 Combine like terms: -24 + 10.02777778 = -13.97222222 10.02777778 + 6.333333333x + x2 = -13.97222222 Factor a perfect square on the left side: (x + 3.166666667)(x + 3.166666667) = -13.97222222 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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