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Simplifying 4250 = 200x + 2x2 Solving 4250 = 200x + 2x2 Solving for variable 'x'. Reorder the terms: 4250 + -200x + -2x2 = 200x + -200x + 2x2 + -2x2 Combine like terms: 200x + -200x = 0 4250 + -200x + -2x2 = 0 + 2x2 + -2x2 4250 + -200x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 4250 + -200x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2125 + -100x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2125 + -100x + -1x2)' equal to zero and attempt to solve: Simplifying 2125 + -100x + -1x2 = 0 Solving 2125 + -100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2125 + 100x + x2 = 0 Move the constant term to the right: Add '2125' to each side of the equation. -2125 + 100x + 2125 + x2 = 0 + 2125 Reorder the terms: -2125 + 2125 + 100x + x2 = 0 + 2125 Combine like terms: -2125 + 2125 = 0 0 + 100x + x2 = 0 + 2125 100x + x2 = 0 + 2125 Combine like terms: 0 + 2125 = 2125 100x + x2 = 2125 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 2125 + 2500 Reorder the terms: 2500 + 100x + x2 = 2125 + 2500 Combine like terms: 2125 + 2500 = 4625 2500 + 100x + x2 = 4625 Factor a perfect square on the left side: (x + 50)(x + 50) = 4625 Calculate the square root of the right side: 68.007352544 Break this problem into two subproblems by setting (x + 50) equal to 68.007352544 and -68.007352544.Subproblem 1
x + 50 = 68.007352544 Simplifying x + 50 = 68.007352544 Reorder the terms: 50 + x = 68.007352544 Solving 50 + x = 68.007352544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 68.007352544 + -50 Combine like terms: 50 + -50 = 0 0 + x = 68.007352544 + -50 x = 68.007352544 + -50 Combine like terms: 68.007352544 + -50 = 18.007352544 x = 18.007352544 Simplifying x = 18.007352544Subproblem 2
x + 50 = -68.007352544 Simplifying x + 50 = -68.007352544 Reorder the terms: 50 + x = -68.007352544 Solving 50 + x = -68.007352544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -68.007352544 + -50 Combine like terms: 50 + -50 = 0 0 + x = -68.007352544 + -50 x = -68.007352544 + -50 Combine like terms: -68.007352544 + -50 = -118.007352544 x = -118.007352544 Simplifying x = -118.007352544Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.007352544, -118.007352544}Solution
x = {18.007352544, -118.007352544}
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