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Simplifying x2 + 699x + -228250 = 0 Reorder the terms: -228250 + 699x + x2 = 0 Solving -228250 + 699x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '228250' to each side of the equation. -228250 + 699x + 228250 + x2 = 0 + 228250 Reorder the terms: -228250 + 228250 + 699x + x2 = 0 + 228250 Combine like terms: -228250 + 228250 = 0 0 + 699x + x2 = 0 + 228250 699x + x2 = 0 + 228250 Combine like terms: 0 + 228250 = 228250 699x + x2 = 228250 The x term is 699x. Take half its coefficient (349.5). Square it (122150.25) and add it to both sides. Add '122150.25' to each side of the equation. 699x + 122150.25 + x2 = 228250 + 122150.25 Reorder the terms: 122150.25 + 699x + x2 = 228250 + 122150.25 Combine like terms: 228250 + 122150.25 = 350400.25 122150.25 + 699x + x2 = 350400.25 Factor a perfect square on the left side: (x + 349.5)(x + 349.5) = 350400.25 Calculate the square root of the right side: 591.946154646 Break this problem into two subproblems by setting (x + 349.5) equal to 591.946154646 and -591.946154646.Subproblem 1
x + 349.5 = 591.946154646 Simplifying x + 349.5 = 591.946154646 Reorder the terms: 349.5 + x = 591.946154646 Solving 349.5 + x = 591.946154646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-349.5' to each side of the equation. 349.5 + -349.5 + x = 591.946154646 + -349.5 Combine like terms: 349.5 + -349.5 = 0.0 0.0 + x = 591.946154646 + -349.5 x = 591.946154646 + -349.5 Combine like terms: 591.946154646 + -349.5 = 242.446154646 x = 242.446154646 Simplifying x = 242.446154646Subproblem 2
x + 349.5 = -591.946154646 Simplifying x + 349.5 = -591.946154646 Reorder the terms: 349.5 + x = -591.946154646 Solving 349.5 + x = -591.946154646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-349.5' to each side of the equation. 349.5 + -349.5 + x = -591.946154646 + -349.5 Combine like terms: 349.5 + -349.5 = 0.0 0.0 + x = -591.946154646 + -349.5 x = -591.946154646 + -349.5 Combine like terms: -591.946154646 + -349.5 = -941.446154646 x = -941.446154646 Simplifying x = -941.446154646Solution
The solution to the problem is based on the solutions from the subproblems. x = {242.446154646, -941.446154646}
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