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Simplifying 12X2 + -640X + 6000 = 0 Reorder the terms: 6000 + -640X + 12X2 = 0 Solving 6000 + -640X + 12X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '4'. 4(1500 + -160X + 3X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1500 + -160X + 3X2)' equal to zero and attempt to solve: Simplifying 1500 + -160X + 3X2 = 0 Solving 1500 + -160X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 500 + -53.33333333X + X2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -53.33333333X + -500 + X2 = 0 + -500 Reorder the terms: 500 + -500 + -53.33333333X + X2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -53.33333333X + X2 = 0 + -500 -53.33333333X + X2 = 0 + -500 Combine like terms: 0 + -500 = -500 -53.33333333X + X2 = -500 The X term is -53.33333333X. Take half its coefficient (-26.66666667). Square it (711.1111113) and add it to both sides. Add '711.1111113' to each side of the equation. -53.33333333X + 711.1111113 + X2 = -500 + 711.1111113 Reorder the terms: 711.1111113 + -53.33333333X + X2 = -500 + 711.1111113 Combine like terms: -500 + 711.1111113 = 211.1111113 711.1111113 + -53.33333333X + X2 = 211.1111113 Factor a perfect square on the left side: (X + -26.66666667)(X + -26.66666667) = 211.1111113 Calculate the square root of the right side: 14.529663152 Break this problem into two subproblems by setting (X + -26.66666667) equal to 14.529663152 and -14.529663152.Subproblem 1
X + -26.66666667 = 14.529663152 Simplifying X + -26.66666667 = 14.529663152 Reorder the terms: -26.66666667 + X = 14.529663152 Solving -26.66666667 + X = 14.529663152 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '26.66666667' to each side of the equation. -26.66666667 + 26.66666667 + X = 14.529663152 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + X = 14.529663152 + 26.66666667 X = 14.529663152 + 26.66666667 Combine like terms: 14.529663152 + 26.66666667 = 41.196329822 X = 41.196329822 Simplifying X = 41.196329822Subproblem 2
X + -26.66666667 = -14.529663152 Simplifying X + -26.66666667 = -14.529663152 Reorder the terms: -26.66666667 + X = -14.529663152 Solving -26.66666667 + X = -14.529663152 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '26.66666667' to each side of the equation. -26.66666667 + 26.66666667 + X = -14.529663152 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + X = -14.529663152 + 26.66666667 X = -14.529663152 + 26.66666667 Combine like terms: -14.529663152 + 26.66666667 = 12.137003518 X = 12.137003518 Simplifying X = 12.137003518Solution
The solution to the problem is based on the solutions from the subproblems. X = {41.196329822, 12.137003518}Solution
X = {41.196329822, 12.137003518}
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