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Simplifying x2 + -228000x + 120000 = 0 Reorder the terms: 120000 + -228000x + x2 = 0 Solving 120000 + -228000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-120000' to each side of the equation. 120000 + -228000x + -120000 + x2 = 0 + -120000 Reorder the terms: 120000 + -120000 + -228000x + x2 = 0 + -120000 Combine like terms: 120000 + -120000 = 0 0 + -228000x + x2 = 0 + -120000 -228000x + x2 = 0 + -120000 Combine like terms: 0 + -120000 = -120000 -228000x + x2 = -120000 The x term is -228000x. Take half its coefficient (-114000). Square it (12996000000) and add it to both sides. Add '12996000000' to each side of the equation. -228000x + 12996000000 + x2 = -120000 + 12996000000 Reorder the terms: 12996000000 + -228000x + x2 = -120000 + 12996000000 Combine like terms: -120000 + 12996000000 = 12995880000 12996000000 + -228000x + x2 = 12995880000 Factor a perfect square on the left side: (x + -114000)(x + -114000) = 12995880000 Calculate the square root of the right side: 113999.473682996 Break this problem into two subproblems by setting (x + -114000) equal to 113999.473682996 and -113999.473682996.Subproblem 1
x + -114000 = 113999.473682996 Simplifying x + -114000 = 113999.473682996 Reorder the terms: -114000 + x = 113999.473682996 Solving -114000 + x = 113999.473682996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '114000' to each side of the equation. -114000 + 114000 + x = 113999.473682996 + 114000 Combine like terms: -114000 + 114000 = 0 0 + x = 113999.473682996 + 114000 x = 113999.473682996 + 114000 Combine like terms: 113999.473682996 + 114000 = 227999.473682996 x = 227999.473682996 Simplifying x = 227999.473682996Subproblem 2
x + -114000 = -113999.473682996 Simplifying x + -114000 = -113999.473682996 Reorder the terms: -114000 + x = -113999.473682996 Solving -114000 + x = -113999.473682996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '114000' to each side of the equation. -114000 + 114000 + x = -113999.473682996 + 114000 Combine like terms: -114000 + 114000 = 0 0 + x = -113999.473682996 + 114000 x = -113999.473682996 + 114000 Combine like terms: -113999.473682996 + 114000 = 0.526317004 x = 0.526317004 Simplifying x = 0.526317004Solution
The solution to the problem is based on the solutions from the subproblems. x = {227999.473682996, 0.526317004}
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