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Simplifying x2 + x + -40000 = 0 Reorder the terms: -40000 + x + x2 = 0 Solving -40000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40000' to each side of the equation. -40000 + x + 40000 + x2 = 0 + 40000 Reorder the terms: -40000 + 40000 + x + x2 = 0 + 40000 Combine like terms: -40000 + 40000 = 0 0 + x + x2 = 0 + 40000 x + x2 = 0 + 40000 Combine like terms: 0 + 40000 = 40000 x + x2 = 40000 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 = 40000 + 0.25 Reorder the terms: 0.25 + x + x2 = 40000 + 0.25 Combine like terms: 40000 + 0.25 = 40000.25 0.25 + x + x2 = 40000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 40000.25 Calculate the square root of the right side: 200.000624999 Break this problem into two subproblems by setting (x + 0.5) equal to 200.000624999 and -200.000624999.Subproblem 1
x + 0.5 = 200.000624999 Simplifying x + 0.5 = 200.000624999 Reorder the terms: 0.5 + x = 200.000624999 Solving 0.5 + x = 200.000624999 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 = 200.000624999 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 200.000624999 + -0.5 x = 200.000624999 + -0.5 Combine like terms: 200.000624999 + -0.5 = 199.500624999 x = 199.500624999 Simplifying x = 199.500624999Subproblem 2
x + 0.5 = -200.000624999 Simplifying x + 0.5 = -200.000624999 Reorder the terms: 0.5 + x = -200.000624999 Solving 0.5 + x = -200.000624999 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 = -200.000624999 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -200.000624999 + -0.5 x = -200.000624999 + -0.5 Combine like terms: -200.000624999 + -0.5 = -200.500624999 x = -200.500624999 Simplifying x = -200.500624999Solution
The solution to the problem is based on the solutions from the subproblems. x = {199.500624999, -200.500624999}
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