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Simplifying 12X(2 + -3X) + -1(5 + 6X) = 11 + 12X (2 * 12X + -3X * 12X) + -1(5 + 6X) = 11 + 12X (24X + -36X2) + -1(5 + 6X) = 11 + 12X 24X + -36X2 + (5 * -1 + 6X * -1) = 11 + 12X 24X + -36X2 + (-5 + -6X) = 11 + 12X Reorder the terms: -5 + 24X + -6X + -36X2 = 11 + 12X Combine like terms: 24X + -6X = 18X -5 + 18X + -36X2 = 11 + 12X Solving -5 + 18X + -36X2 = 11 + 12X Solving for variable 'X'. Reorder the terms: -5 + -11 + 18X + -12X + -36X2 = 11 + 12X + -11 + -12X Combine like terms: -5 + -11 = -16 -16 + 18X + -12X + -36X2 = 11 + 12X + -11 + -12X Combine like terms: 18X + -12X = 6X -16 + 6X + -36X2 = 11 + 12X + -11 + -12X Reorder the terms: -16 + 6X + -36X2 = 11 + -11 + 12X + -12X Combine like terms: 11 + -11 = 0 -16 + 6X + -36X2 = 0 + 12X + -12X -16 + 6X + -36X2 = 12X + -12X Combine like terms: 12X + -12X = 0 -16 + 6X + -36X2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 3X + -18X2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 3X + -18X2)' equal to zero and attempt to solve: Simplifying -8 + 3X + -18X2 = 0 Solving -8 + 3X + -18X2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 0.4444444444 + -0.1666666667X + X2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.1666666667X + -0.4444444444 + X2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.1666666667X + X2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.1666666667X + X2 = 0 + -0.4444444444 -0.1666666667X + X2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.1666666667X + X2 = -0.4444444444 The X term is -0.1666666667X. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667X + 0.006944444447 + X2 = -0.4444444444 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667X + X2 = -0.4444444444 + 0.006944444447 Combine like terms: -0.4444444444 + 0.006944444447 = -0.437499999953 0.006944444447 + -0.1666666667X + X2 = -0.437499999953 Factor a perfect square on the left side: (X + -0.08333333335)(X + -0.08333333335) = -0.437499999953 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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