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Simplifying x2 + 50x + -625 = 0 Reorder the terms: -625 + 50x + x2 = 0 Solving -625 + 50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '625' to each side of the equation. -625 + 50x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + 50x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + 50x + x2 = 0 + 625 50x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 50x + x2 = 625 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 = 625 + 625 Reorder the terms: 625 + 50x + x2 = 625 + 625 Combine like terms: 625 + 625 = 1250 625 + 50x + x2 = 1250 Factor a perfect square on the left side: (x + 25)(x + 25) = 1250 Calculate the square root of the right side: 35.355339059 Break this problem into two subproblems by setting (x + 25) equal to 35.355339059 and -35.355339059.Subproblem 1
x + 25 = 35.355339059 Simplifying x + 25 = 35.355339059 Reorder the terms: 25 + x = 35.355339059 Solving 25 + x = 35.355339059 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 = 35.355339059 + -25 Combine like terms: 25 + -25 = 0 0 + x = 35.355339059 + -25 x = 35.355339059 + -25 Combine like terms: 35.355339059 + -25 = 10.355339059 x = 10.355339059 Simplifying x = 10.355339059Subproblem 2
x + 25 = -35.355339059 Simplifying x + 25 = -35.355339059 Reorder the terms: 25 + x = -35.355339059 Solving 25 + x = -35.355339059 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 = -35.355339059 + -25 Combine like terms: 25 + -25 = 0 0 + x = -35.355339059 + -25 x = -35.355339059 + -25 Combine like terms: -35.355339059 + -25 = -60.355339059 x = -60.355339059 Simplifying x = -60.355339059Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.355339059, -60.355339059}
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