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Simplifying x2 + 51x + -50 = 0 Reorder the terms: -50 + 51x + x2 = 0 Solving -50 + 51x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 51x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 51x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 51x + x2 = 0 + 50 51x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 51x + x2 = 50 The x term is 51x. Take half its coefficient (25.5). Square it (650.25) and add it to both sides. Add '650.25' to each side of the equation. 51x + 650.25 + x2 = 50 + 650.25 Reorder the terms: 650.25 + 51x + x2 = 50 + 650.25 Combine like terms: 50 + 650.25 = 700.25 650.25 + 51x + x2 = 700.25 Factor a perfect square on the left side: (x + 25.5)(x + 25.5) = 700.25 Calculate the square root of the right side: 26.462237245 Break this problem into two subproblems by setting (x + 25.5) equal to 26.462237245 and -26.462237245.Subproblem 1
x + 25.5 = 26.462237245 Simplifying x + 25.5 = 26.462237245 Reorder the terms: 25.5 + x = 26.462237245 Solving 25.5 + x = 26.462237245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = 26.462237245 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = 26.462237245 + -25.5 x = 26.462237245 + -25.5 Combine like terms: 26.462237245 + -25.5 = 0.962237245 x = 0.962237245 Simplifying x = 0.962237245Subproblem 2
x + 25.5 = -26.462237245 Simplifying x + 25.5 = -26.462237245 Reorder the terms: 25.5 + x = -26.462237245 Solving 25.5 + x = -26.462237245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25.5' to each side of the equation. 25.5 + -25.5 + x = -26.462237245 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + x = -26.462237245 + -25.5 x = -26.462237245 + -25.5 Combine like terms: -26.462237245 + -25.5 = -51.962237245 x = -51.962237245 Simplifying x = -51.962237245Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.962237245, -51.962237245}
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