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Simplifying x2 + x + -10000 = 0 Reorder the terms: -10000 + x + x2 = 0 Solving -10000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + x + x2 = 0 + 10000 x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 x + x2 = 10000 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 10000 + 0.25 Reorder the terms: 0.25 + x + x2 = 10000 + 0.25 Combine like terms: 10000 + 0.25 = 10000.25 0.25 + x + x2 = 10000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 10000.25 Calculate the square root of the right side: 100.001249992 Break this problem into two subproblems by setting (x + 0.5) equal to 100.001249992 and -100.001249992.Subproblem 1
x + 0.5 = 100.001249992 Simplifying x + 0.5 = 100.001249992 Reorder the terms: 0.5 + x = 100.001249992 Solving 0.5 + x = 100.001249992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 100.001249992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 100.001249992 + -0.5 x = 100.001249992 + -0.5 Combine like terms: 100.001249992 + -0.5 = 99.501249992 x = 99.501249992 Simplifying x = 99.501249992Subproblem 2
x + 0.5 = -100.001249992 Simplifying x + 0.5 = -100.001249992 Reorder the terms: 0.5 + x = -100.001249992 Solving 0.5 + x = -100.001249992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -100.001249992 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -100.001249992 + -0.5 x = -100.001249992 + -0.5 Combine like terms: -100.001249992 + -0.5 = -100.501249992 x = -100.501249992 Simplifying x = -100.501249992Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.501249992, -100.501249992}
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