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Simplifying x2 + -50x + -49 = 0 Reorder the terms: -49 + -50x + x2 = 0 Solving -49 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -50x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -50x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -50x + x2 = 0 + 49 -50x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -50x + x2 = 49 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 = 49 + 625 Reorder the terms: 625 + -50x + x2 = 49 + 625 Combine like terms: 49 + 625 = 674 625 + -50x + x2 = 674 Factor a perfect square on the left side: (x + -25)(x + -25) = 674 Calculate the square root of the right side: 25.961509971 Break this problem into two subproblems by setting (x + -25) equal to 25.961509971 and -25.961509971.Subproblem 1
x + -25 = 25.961509971 Simplifying x + -25 = 25.961509971 Reorder the terms: -25 + x = 25.961509971 Solving -25 + x = 25.961509971 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 = 25.961509971 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.961509971 + 25 x = 25.961509971 + 25 Combine like terms: 25.961509971 + 25 = 50.961509971 x = 50.961509971 Simplifying x = 50.961509971Subproblem 2
x + -25 = -25.961509971 Simplifying x + -25 = -25.961509971 Reorder the terms: -25 + x = -25.961509971 Solving -25 + x = -25.961509971 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 = -25.961509971 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.961509971 + 25 x = -25.961509971 + 25 Combine like terms: -25.961509971 + 25 = -0.961509971 x = -0.961509971 Simplifying x = -0.961509971Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.961509971, -0.961509971}
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