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Simplifying 36x(x + -1) + -6x + 21 = 0 Reorder the terms: 36x(-1 + x) + -6x + 21 = 0 (-1 * 36x + x * 36x) + -6x + 21 = 0 (-36x + 36x2) + -6x + 21 = 0 Reorder the terms: 21 + -36x + -6x + 36x2 = 0 Combine like terms: -36x + -6x = -42x 21 + -42x + 36x2 = 0 Solving 21 + -42x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -14x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -14x + 12x2)' equal to zero and attempt to solve: Simplifying 7 + -14x + 12x2 = 0 Solving 7 + -14x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + -1.166666667x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + -1.166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + -0.5833333333 -1.166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 -1.166666667x + x2 = -0.5833333333 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 = -0.5833333333 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = -0.5833333333 + 0.3402777780 Combine like terms: -0.5833333333 + 0.3402777780 = -0.2430555553 0.3402777780 + -1.166666667x + x2 = -0.2430555553 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = -0.2430555553 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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