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Simplifying x2 + x + -60000 = 0 Reorder the terms: -60000 + x + x2 = 0 Solving -60000 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60000' to each side of the equation. -60000 + x + 60000 + x2 = 0 + 60000 Reorder the terms: -60000 + 60000 + x + x2 = 0 + 60000 Combine like terms: -60000 + 60000 = 0 0 + x + x2 = 0 + 60000 x + x2 = 0 + 60000 Combine like terms: 0 + 60000 = 60000 x + x2 = 60000 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 = 60000 + 0.25 Reorder the terms: 0.25 + x + x2 = 60000 + 0.25 Combine like terms: 60000 + 0.25 = 60000.25 0.25 + x + x2 = 60000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 60000.25 Calculate the square root of the right side: 244.949484588 Break this problem into two subproblems by setting (x + 0.5) equal to 244.949484588 and -244.949484588.Subproblem 1
x + 0.5 = 244.949484588 Simplifying x + 0.5 = 244.949484588 Reorder the terms: 0.5 + x = 244.949484588 Solving 0.5 + x = 244.949484588 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 = 244.949484588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 244.949484588 + -0.5 x = 244.949484588 + -0.5 Combine like terms: 244.949484588 + -0.5 = 244.449484588 x = 244.449484588 Simplifying x = 244.449484588Subproblem 2
x + 0.5 = -244.949484588 Simplifying x + 0.5 = -244.949484588 Reorder the terms: 0.5 + x = -244.949484588 Solving 0.5 + x = -244.949484588 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 = -244.949484588 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -244.949484588 + -0.5 x = -244.949484588 + -0.5 Combine like terms: -244.949484588 + -0.5 = -245.449484588 x = -245.449484588 Simplifying x = -245.449484588Solution
The solution to the problem is based on the solutions from the subproblems. x = {244.449484588, -245.449484588}
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