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Simplifying 4X + 8X(200 + -1X) = 1056 4X + (200 * 8X + -1X * 8X) = 1056 4X + (1600X + -8X2) = 1056 Combine like terms: 4X + 1600X = 1604X 1604X + -8X2 = 1056 Solving 1604X + -8X2 = 1056 Solving for variable 'X'. Reorder the terms: -1056 + 1604X + -8X2 = 1056 + -1056 Combine like terms: 1056 + -1056 = 0 -1056 + 1604X + -8X2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-264 + 401X + -2X2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-264 + 401X + -2X2)' equal to zero and attempt to solve: Simplifying -264 + 401X + -2X2 = 0 Solving -264 + 401X + -2X2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 132 + -200.5X + X2 = 0 Move the constant term to the right: Add '-132' to each side of the equation. 132 + -200.5X + -132 + X2 = 0 + -132 Reorder the terms: 132 + -132 + -200.5X + X2 = 0 + -132 Combine like terms: 132 + -132 = 0 0 + -200.5X + X2 = 0 + -132 -200.5X + X2 = 0 + -132 Combine like terms: 0 + -132 = -132 -200.5X + X2 = -132 The X term is -200.5X. Take half its coefficient (-100.25). Square it (10050.0625) and add it to both sides. Add '10050.0625' to each side of the equation. -200.5X + 10050.0625 + X2 = -132 + 10050.0625 Reorder the terms: 10050.0625 + -200.5X + X2 = -132 + 10050.0625 Combine like terms: -132 + 10050.0625 = 9918.0625 10050.0625 + -200.5X + X2 = 9918.0625 Factor a perfect square on the left side: (X + -100.25)(X + -100.25) = 9918.0625 Calculate the square root of the right side: 99.589469825 Break this problem into two subproblems by setting (X + -100.25) equal to 99.589469825 and -99.589469825.Subproblem 1
X + -100.25 = 99.589469825 Simplifying X + -100.25 = 99.589469825 Reorder the terms: -100.25 + X = 99.589469825 Solving -100.25 + X = 99.589469825 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '100.25' to each side of the equation. -100.25 + 100.25 + X = 99.589469825 + 100.25 Combine like terms: -100.25 + 100.25 = 0.00 0.00 + X = 99.589469825 + 100.25 X = 99.589469825 + 100.25 Combine like terms: 99.589469825 + 100.25 = 199.839469825 X = 199.839469825 Simplifying X = 199.839469825Subproblem 2
X + -100.25 = -99.589469825 Simplifying X + -100.25 = -99.589469825 Reorder the terms: -100.25 + X = -99.589469825 Solving -100.25 + X = -99.589469825 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '100.25' to each side of the equation. -100.25 + 100.25 + X = -99.589469825 + 100.25 Combine like terms: -100.25 + 100.25 = 0.00 0.00 + X = -99.589469825 + 100.25 X = -99.589469825 + 100.25 Combine like terms: -99.589469825 + 100.25 = 0.660530175 X = 0.660530175 Simplifying X = 0.660530175Solution
The solution to the problem is based on the solutions from the subproblems. X = {199.839469825, 0.660530175}Solution
X = {199.839469825, 0.660530175}
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