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Simplifying (x)(x + -5) = 277 Reorder the terms: x(-5 + x) = 277 (-5 * x + x * x) = 277 (-5x + x2) = 277 Solving -5x + x2 = 277 Solving for variable 'x'. Reorder the terms: -277 + -5x + x2 = 277 + -277 Combine like terms: 277 + -277 = 0 -277 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '277' to each side of the equation. -277 + -5x + 277 + x2 = 0 + 277 Reorder the terms: -277 + 277 + -5x + x2 = 0 + 277 Combine like terms: -277 + 277 = 0 0 + -5x + x2 = 0 + 277 -5x + x2 = 0 + 277 Combine like terms: 0 + 277 = 277 -5x + x2 = 277 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 277 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 277 + 6.25 Combine like terms: 277 + 6.25 = 283.25 6.25 + -5x + x2 = 283.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 283.25 Calculate the square root of the right side: 16.83003268 Break this problem into two subproblems by setting (x + -2.5) equal to 16.83003268 and -16.83003268.Subproblem 1
x + -2.5 = 16.83003268 Simplifying x + -2.5 = 16.83003268 Reorder the terms: -2.5 + x = 16.83003268 Solving -2.5 + x = 16.83003268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 16.83003268 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 16.83003268 + 2.5 x = 16.83003268 + 2.5 Combine like terms: 16.83003268 + 2.5 = 19.33003268 x = 19.33003268 Simplifying x = 19.33003268Subproblem 2
x + -2.5 = -16.83003268 Simplifying x + -2.5 = -16.83003268 Reorder the terms: -2.5 + x = -16.83003268 Solving -2.5 + x = -16.83003268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -16.83003268 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -16.83003268 + 2.5 x = -16.83003268 + 2.5 Combine like terms: -16.83003268 + 2.5 = -14.33003268 x = -14.33003268 Simplifying x = -14.33003268Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.33003268, -14.33003268}
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