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Simplifying 6x2 + 16x + 94 = 0 Reorder the terms: 94 + 16x + 6x2 = 0 Solving 94 + 16x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(47 + 8x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(47 + 8x + 3x2)' equal to zero and attempt to solve: Simplifying 47 + 8x + 3x2 = 0 Solving 47 + 8x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.66666667 + 2.666666667x + x2 = 0 Move the constant term to the right: Add '-15.66666667' to each side of the equation. 15.66666667 + 2.666666667x + -15.66666667 + x2 = 0 + -15.66666667 Reorder the terms: 15.66666667 + -15.66666667 + 2.666666667x + x2 = 0 + -15.66666667 Combine like terms: 15.66666667 + -15.66666667 = 0.00000000 0.00000000 + 2.666666667x + x2 = 0 + -15.66666667 2.666666667x + x2 = 0 + -15.66666667 Combine like terms: 0 + -15.66666667 = -15.66666667 2.666666667x + x2 = -15.66666667 The x term is 2.666666667x. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x + 1.777777780 + x2 = -15.66666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x + x2 = -15.66666667 + 1.777777780 Combine like terms: -15.66666667 + 1.777777780 = -13.88888889 1.777777780 + 2.666666667x + x2 = -13.88888889 Factor a perfect square on the left side: (x + 1.333333334)(x + 1.333333334) = -13.88888889 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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