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Simplifying x[148201 + x] = 629 [148201 * x + x * x] = 629 [148201x + x2] = 629 Solving 148201x + x2 = 629 Solving for variable 'x'. Reorder the terms: -629 + 148201x + x2 = 629 + -629 Combine like terms: 629 + -629 = 0 -629 + 148201x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '629' to each side of the equation. -629 + 148201x + 629 + x2 = 0 + 629 Reorder the terms: -629 + 629 + 148201x + x2 = 0 + 629 Combine like terms: -629 + 629 = 0 0 + 148201x + x2 = 0 + 629 148201x + x2 = 0 + 629 Combine like terms: 0 + 629 = 629 148201x + x2 = 629 The x term is 148201x. Take half its coefficient (74100.5). Square it (5490884100) and add it to both sides. Add '5490884100' to each side of the equation. 148201x + 5490884100 + x2 = 629 + 5490884100 Reorder the terms: 5490884100 + 148201x + x2 = 629 + 5490884100 Combine like terms: 629 + 5490884100 = 5490884729 5490884100 + 148201x + x2 = 5490884729 Factor a perfect square on the left side: (x + 74100.5)(x + 74100.5) = 5490884729 Calculate the square root of the right side: 74100.504242549 Break this problem into two subproblems by setting (x + 74100.5) equal to 74100.504242549 and -74100.504242549.Subproblem 1
x + 74100.5 = 74100.504242549 Simplifying x + 74100.5 = 74100.504242549 Reorder the terms: 74100.5 + x = 74100.504242549 Solving 74100.5 + x = 74100.504242549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-74100.5' to each side of the equation. 74100.5 + -74100.5 + x = 74100.504242549 + -74100.5 Combine like terms: 74100.5 + -74100.5 = 0.0 0.0 + x = 74100.504242549 + -74100.5 x = 74100.504242549 + -74100.5 Combine like terms: 74100.504242549 + -74100.5 = 0.004242549 x = 0.004242549 Simplifying x = 0.004242549Subproblem 2
x + 74100.5 = -74100.504242549 Simplifying x + 74100.5 = -74100.504242549 Reorder the terms: 74100.5 + x = -74100.504242549 Solving 74100.5 + x = -74100.504242549 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-74100.5' to each side of the equation. 74100.5 + -74100.5 + x = -74100.504242549 + -74100.5 Combine like terms: 74100.5 + -74100.5 = 0.0 0.0 + x = -74100.504242549 + -74100.5 x = -74100.504242549 + -74100.5 Combine like terms: -74100.504242549 + -74100.5 = -148201.004242549 x = -148201.004242549 Simplifying x = -148201.004242549Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.004242549, -148201.004242549}
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