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Simplifying 0 = 6x2 + 2x + 16 Reorder the terms: 0 = 16 + 2x + 6x2 Solving 0 = 16 + 2x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -16 = -16 -16 + -2x + -6x2 = 16 + 2x + 6x2 + -16 + -2x + -6x2 Reorder the terms: -16 + -2x + -6x2 = 16 + -16 + 2x + -2x + 6x2 + -6x2 Combine like terms: 16 + -16 = 0 -16 + -2x + -6x2 = 0 + 2x + -2x + 6x2 + -6x2 -16 + -2x + -6x2 = 2x + -2x + 6x2 + -6x2 Combine like terms: 2x + -2x = 0 -16 + -2x + -6x2 = 0 + 6x2 + -6x2 -16 + -2x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -16 + -2x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(8 + x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(8 + x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + x + 3x2 = 0 Solving 8 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + 0.3333333333x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + 0.3333333333x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + 0.3333333333x + x2 = 0 + -2.666666667 0.3333333333x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 0.3333333333x + x2 = -2.666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = -2.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -2.666666667 + 0.25 Combine like terms: -2.666666667 + 0.25 = -2.416666667 0.25 + 0.3333333333x + x2 = -2.416666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.416666667 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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