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Simplifying 12x = 6x2 + 8 Reorder the terms: 12x = 8 + 6x2 Solving 12x = 8 + 6x2 Solving for variable 'x'. Reorder the terms: -8 + 12x + -6x2 = 8 + 6x2 + -8 + -6x2 Reorder the terms: -8 + 12x + -6x2 = 8 + -8 + 6x2 + -6x2 Combine like terms: 8 + -8 = 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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