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Simplifying 875000 = 10000X2 + 45000X Reorder the terms: 875000 = 45000X + 10000X2 Solving 875000 = 45000X + 10000X2 Solving for variable 'X'. Reorder the terms: 875000 + -45000X + -10000X2 = 45000X + -45000X + 10000X2 + -10000X2 Combine like terms: 45000X + -45000X = 0 875000 + -45000X + -10000X2 = 0 + 10000X2 + -10000X2 875000 + -45000X + -10000X2 = 10000X2 + -10000X2 Combine like terms: 10000X2 + -10000X2 = 0 875000 + -45000X + -10000X2 = 0 Factor out the Greatest Common Factor (GCF), '5000'. 5000(175 + -9X + -2X2) = 0 Ignore the factor 5000.Subproblem 1
Set the factor '(175 + -9X + -2X2)' equal to zero and attempt to solve: Simplifying 175 + -9X + -2X2 = 0 Solving 175 + -9X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -87.5 + 4.5X + X2 = 0 Move the constant term to the right: Add '87.5' to each side of the equation. -87.5 + 4.5X + 87.5 + X2 = 0 + 87.5 Reorder the terms: -87.5 + 87.5 + 4.5X + X2 = 0 + 87.5 Combine like terms: -87.5 + 87.5 = 0.0 0.0 + 4.5X + X2 = 0 + 87.5 4.5X + X2 = 0 + 87.5 Combine like terms: 0 + 87.5 = 87.5 4.5X + X2 = 87.5 The X term is 4.5X. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5X + 5.0625 + X2 = 87.5 + 5.0625 Reorder the terms: 5.0625 + 4.5X + X2 = 87.5 + 5.0625 Combine like terms: 87.5 + 5.0625 = 92.5625 5.0625 + 4.5X + X2 = 92.5625 Factor a perfect square on the left side: (X + 2.25)(X + 2.25) = 92.5625 Calculate the square root of the right side: 9.620940702 Break this problem into two subproblems by setting (X + 2.25) equal to 9.620940702 and -9.620940702.Subproblem 1
X + 2.25 = 9.620940702 Simplifying X + 2.25 = 9.620940702 Reorder the terms: 2.25 + X = 9.620940702 Solving 2.25 + X = 9.620940702 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + X = 9.620940702 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = 9.620940702 + -2.25 X = 9.620940702 + -2.25 Combine like terms: 9.620940702 + -2.25 = 7.370940702 X = 7.370940702 Simplifying X = 7.370940702Subproblem 2
X + 2.25 = -9.620940702 Simplifying X + 2.25 = -9.620940702 Reorder the terms: 2.25 + X = -9.620940702 Solving 2.25 + X = -9.620940702 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + X = -9.620940702 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + X = -9.620940702 + -2.25 X = -9.620940702 + -2.25 Combine like terms: -9.620940702 + -2.25 = -11.870940702 X = -11.870940702 Simplifying X = -11.870940702Solution
The solution to the problem is based on the solutions from the subproblems. X = {7.370940702, -11.870940702}Solution
X = {7.370940702, -11.870940702}
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