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Simplifying 12X2 + -64X + 60 = 0 Reorder the terms: 60 + -64X + 12X2 = 0 Solving 60 + -64X + 12X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(15 + -16X + 3X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15 + -16X + 3X2)' equal to zero and attempt to solve: Simplifying 15 + -16X + 3X2 = 0 Solving 15 + -16X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5 + -5.333333333X + X2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5.333333333X + -5 + X2 = 0 + -5 Reorder the terms: 5 + -5 + -5.333333333X + X2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5.333333333X + X2 = 0 + -5 -5.333333333X + X2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5.333333333X + X2 = -5 The X term is -5.333333333X. Take half its coefficient (-2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. -5.333333333X + 7.111111113 + X2 = -5 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333X + X2 = -5 + 7.111111113 Combine like terms: -5 + 7.111111113 = 2.111111113 7.111111113 + -5.333333333X + X2 = 2.111111113 Factor a perfect square on the left side: (X + -2.666666667)(X + -2.666666667) = 2.111111113 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (X + -2.666666667) equal to 1.452966315 and -1.452966315.Subproblem 1
X + -2.666666667 = 1.452966315 Simplifying X + -2.666666667 = 1.452966315 Reorder the terms: -2.666666667 + X = 1.452966315 Solving -2.666666667 + X = 1.452966315 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + X = 1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + X = 1.452966315 + 2.666666667 X = 1.452966315 + 2.666666667 Combine like terms: 1.452966315 + 2.666666667 = 4.119632982 X = 4.119632982 Simplifying X = 4.119632982Subproblem 2
X + -2.666666667 = -1.452966315 Simplifying X + -2.666666667 = -1.452966315 Reorder the terms: -2.666666667 + X = -1.452966315 Solving -2.666666667 + X = -1.452966315 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + X = -1.452966315 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + X = -1.452966315 + 2.666666667 X = -1.452966315 + 2.666666667 Combine like terms: -1.452966315 + 2.666666667 = 1.213700352 X = 1.213700352 Simplifying X = 1.213700352Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.119632982, 1.213700352}Solution
X = {4.119632982, 1.213700352}
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