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Simplifying x2 + 50x + -61 = 0 Reorder the terms: -61 + 50x + x2 = 0 Solving -61 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 50x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 50x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 50x + x2 = 0 + 61 50x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 50x + x2 = 61 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 61 + 625 Reorder the terms: 625 + 50x + x2 = 61 + 625 Combine like terms: 61 + 625 = 686 625 + 50x + x2 = 686 Factor a perfect square on the left side: (x + 25)(x + 25) = 686 Calculate the square root of the right side: 26.191601707 Break this problem into two subproblems by setting (x + 25) equal to 26.191601707 and -26.191601707.Subproblem 1
x + 25 = 26.191601707 Simplifying x + 25 = 26.191601707 Reorder the terms: 25 + x = 26.191601707 Solving 25 + x = 26.191601707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 26.191601707 + -25 Combine like terms: 25 + -25 = 0 0 + x = 26.191601707 + -25 x = 26.191601707 + -25 Combine like terms: 26.191601707 + -25 = 1.191601707 x = 1.191601707 Simplifying x = 1.191601707Subproblem 2
x + 25 = -26.191601707 Simplifying x + 25 = -26.191601707 Reorder the terms: 25 + x = -26.191601707 Solving 25 + x = -26.191601707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -26.191601707 + -25 Combine like terms: 25 + -25 = 0 0 + x = -26.191601707 + -25 x = -26.191601707 + -25 Combine like terms: -26.191601707 + -25 = -51.191601707 x = -51.191601707 Simplifying x = -51.191601707Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.191601707, -51.191601707}
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