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Simplifying x2 + -5x + -7750 = 0 Reorder the terms: -7750 + -5x + x2 = 0 Solving -7750 + -5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7750' to each side of the equation. -7750 + -5x + 7750 + x2 = 0 + 7750 Reorder the terms: -7750 + 7750 + -5x + x2 = 0 + 7750 Combine like terms: -7750 + 7750 = 0 0 + -5x + x2 = 0 + 7750 -5x + x2 = 0 + 7750 Combine like terms: 0 + 7750 = 7750 -5x + x2 = 7750 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 = 7750 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7750 + 6.25 Combine like terms: 7750 + 6.25 = 7756.25 6.25 + -5x + x2 = 7756.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7756.25 Calculate the square root of the right side: 88.069574769 Break this problem into two subproblems by setting (x + -2.5) equal to 88.069574769 and -88.069574769.Subproblem 1
x + -2.5 = 88.069574769 Simplifying x + -2.5 = 88.069574769 Reorder the terms: -2.5 + x = 88.069574769 Solving -2.5 + x = 88.069574769 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 = 88.069574769 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 88.069574769 + 2.5 x = 88.069574769 + 2.5 Combine like terms: 88.069574769 + 2.5 = 90.569574769 x = 90.569574769 Simplifying x = 90.569574769Subproblem 2
x + -2.5 = -88.069574769 Simplifying x + -2.5 = -88.069574769 Reorder the terms: -2.5 + x = -88.069574769 Solving -2.5 + x = -88.069574769 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 = -88.069574769 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -88.069574769 + 2.5 x = -88.069574769 + 2.5 Combine like terms: -88.069574769 + 2.5 = -85.569574769 x = -85.569574769 Simplifying x = -85.569574769Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.569574769, -85.569574769}
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