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Simplifying 0 = 6x2 + 12x + 8 Reorder the terms: 0 = 8 + 12x + 6x2 Solving 0 = 8 + 12x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + -12x + -6x2 = 8 + 12x + 6x2 + -8 + -12x + -6x2 Reorder the terms: -8 + -12x + -6x2 = 8 + -8 + 12x + -12x + 6x2 + -6x2 Combine like terms: 8 + -8 = 0 -8 + -12x + -6x2 = 0 + 12x + -12x + 6x2 + -6x2 -8 + -12x + -6x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 -8 + -12x + -6x2 = 0 + 6x2 + -6x2 -8 + -12x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -8 + -12x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(4 + 6x + 3x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(4 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 6x + 3x2 = 0 Solving 4 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + -1.333333333 2x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2x + x2 = -1.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.333333333 + 1 Reorder the terms: 1 + 2x + x2 = -1.333333333 + 1 Combine like terms: -1.333333333 + 1 = -0.333333333 1 + 2x + x2 = -0.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.333333333 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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