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Simplifying x2 + 275x + -3850 = 0 Reorder the terms: -3850 + 275x + x2 = 0 Solving -3850 + 275x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3850' to each side of the equation. -3850 + 275x + 3850 + x2 = 0 + 3850 Reorder the terms: -3850 + 3850 + 275x + x2 = 0 + 3850 Combine like terms: -3850 + 3850 = 0 0 + 275x + x2 = 0 + 3850 275x + x2 = 0 + 3850 Combine like terms: 0 + 3850 = 3850 275x + x2 = 3850 The x term is 275x. Take half its coefficient (137.5). Square it (18906.25) and add it to both sides. Add '18906.25' to each side of the equation. 275x + 18906.25 + x2 = 3850 + 18906.25 Reorder the terms: 18906.25 + 275x + x2 = 3850 + 18906.25 Combine like terms: 3850 + 18906.25 = 22756.25 18906.25 + 275x + x2 = 22756.25 Factor a perfect square on the left side: (x + 137.5)(x + 137.5) = 22756.25 Calculate the square root of the right side: 150.851748415 Break this problem into two subproblems by setting (x + 137.5) equal to 150.851748415 and -150.851748415.Subproblem 1
x + 137.5 = 150.851748415 Simplifying x + 137.5 = 150.851748415 Reorder the terms: 137.5 + x = 150.851748415 Solving 137.5 + x = 150.851748415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-137.5' to each side of the equation. 137.5 + -137.5 + x = 150.851748415 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + x = 150.851748415 + -137.5 x = 150.851748415 + -137.5 Combine like terms: 150.851748415 + -137.5 = 13.351748415 x = 13.351748415 Simplifying x = 13.351748415Subproblem 2
x + 137.5 = -150.851748415 Simplifying x + 137.5 = -150.851748415 Reorder the terms: 137.5 + x = -150.851748415 Solving 137.5 + x = -150.851748415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-137.5' to each side of the equation. 137.5 + -137.5 + x = -150.851748415 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + x = -150.851748415 + -137.5 x = -150.851748415 + -137.5 Combine like terms: -150.851748415 + -137.5 = -288.351748415 x = -288.351748415 Simplifying x = -288.351748415Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.351748415, -288.351748415}
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