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Simplifying 12x2 + -14x + 16 = 0 Reorder the terms: 16 + -14x + 12x2 = 0 Solving 16 + -14x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -7x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -7x + 6x2)' equal to zero and attempt to solve: Simplifying 8 + -7x + 6x2 = 0 Solving 8 + -7x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -1.166666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -1.166666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -1.166666667x + x2 = 0 + -1.333333333 -1.166666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -1.166666667x + x2 = -1.333333333 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = -1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -1.333333333 + 0.3402777780 Combine like terms: -1.333333333 + 0.3402777780 = -0.993055555 0.3402777780 + -1.166666667x + x2 = -0.993055555 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = -0.993055555 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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