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Simplifying 10000 = x2 + 2x Reorder the terms: 10000 = 2x + x2 Solving 10000 = 2x + x2 Solving for variable 'x'. Reorder the terms: 10000 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 10000 + -2x + -1x2 = 0 + x2 + -1x2 10000 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10000 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10000 + 2x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 2x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 2x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 2x + x2 = 0 + 10000 2x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 2x + x2 = 10000 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10000 + 1 Reorder the terms: 1 + 2x + x2 = 10000 + 1 Combine like terms: 10000 + 1 = 10001 1 + 2x + x2 = 10001 Factor a perfect square on the left side: (x + 1)(x + 1) = 10001 Calculate the square root of the right side: 100.004999875 Break this problem into two subproblems by setting (x + 1) equal to 100.004999875 and -100.004999875.Subproblem 1
x + 1 = 100.004999875 Simplifying x + 1 = 100.004999875 Reorder the terms: 1 + x = 100.004999875 Solving 1 + x = 100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 100.004999875 + -1 Combine like terms: 1 + -1 = 0 0 + x = 100.004999875 + -1 x = 100.004999875 + -1 Combine like terms: 100.004999875 + -1 = 99.004999875 x = 99.004999875 Simplifying x = 99.004999875Subproblem 2
x + 1 = -100.004999875 Simplifying x + 1 = -100.004999875 Reorder the terms: 1 + x = -100.004999875 Solving 1 + x = -100.004999875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -100.004999875 + -1 Combine like terms: 1 + -1 = 0 0 + x = -100.004999875 + -1 x = -100.004999875 + -1 Combine like terms: -100.004999875 + -1 = -101.004999875 x = -101.004999875 Simplifying x = -101.004999875Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.004999875, -101.004999875}
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