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Simplifying x2 + 275x + -4400 = 0 Reorder the terms: -4400 + 275x + x2 = 0 Solving -4400 + 275x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4400' to each side of the equation. -4400 + 275x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + 275x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + 275x + x2 = 0 + 4400 275x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 275x + x2 = 4400 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 = 4400 + 18906.25 Reorder the terms: 18906.25 + 275x + x2 = 4400 + 18906.25 Combine like terms: 4400 + 18906.25 = 23306.25 18906.25 + 275x + x2 = 23306.25 Factor a perfect square on the left side: (x + 137.5)(x + 137.5) = 23306.25 Calculate the square root of the right side: 152.663846408 Break this problem into two subproblems by setting (x + 137.5) equal to 152.663846408 and -152.663846408.Subproblem 1
x + 137.5 = 152.663846408 Simplifying x + 137.5 = 152.663846408 Reorder the terms: 137.5 + x = 152.663846408 Solving 137.5 + x = 152.663846408 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 = 152.663846408 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + x = 152.663846408 + -137.5 x = 152.663846408 + -137.5 Combine like terms: 152.663846408 + -137.5 = 15.163846408 x = 15.163846408 Simplifying x = 15.163846408Subproblem 2
x + 137.5 = -152.663846408 Simplifying x + 137.5 = -152.663846408 Reorder the terms: 137.5 + x = -152.663846408 Solving 137.5 + x = -152.663846408 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 = -152.663846408 + -137.5 Combine like terms: 137.5 + -137.5 = 0.0 0.0 + x = -152.663846408 + -137.5 x = -152.663846408 + -137.5 Combine like terms: -152.663846408 + -137.5 = -290.163846408 x = -290.163846408 Simplifying x = -290.163846408Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.163846408, -290.163846408}
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