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Simplifying 6x2 + 14 = 2x Reorder the terms: 14 + 6x2 = 2x Solving 14 + 6x2 = 2x Solving for variable 'x'. Reorder the terms: 14 + -2x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 14 + -2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -1x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -1x + 3x2)' equal to zero and attempt to solve: Simplifying 7 + -1x + 3x2 = 0 Solving 7 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -0.3333333333x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -0.3333333333x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -0.3333333333x + x2 = 0 + -2.333333333 -0.3333333333x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -0.3333333333x + x2 = -2.333333333 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = -2.333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = -2.333333333 + 0.02777777779 Combine like terms: -2.333333333 + 0.02777777779 = -2.30555555521 0.02777777779 + -0.3333333333x + x2 = -2.30555555521 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = -2.30555555521 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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