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Simplifying x2 + -50x = 60 Reorder the terms: -50x + x2 = 60 Solving -50x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -50x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -50x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -50x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -50x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -50x + x2 = 0 + 60 -50x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -50x + x2 = 60 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 = 60 + 625 Reorder the terms: 625 + -50x + x2 = 60 + 625 Combine like terms: 60 + 625 = 685 625 + -50x + x2 = 685 Factor a perfect square on the left side: (x + -25)(x + -25) = 685 Calculate the square root of the right side: 26.172504657 Break this problem into two subproblems by setting (x + -25) equal to 26.172504657 and -26.172504657.Subproblem 1
x + -25 = 26.172504657 Simplifying x + -25 = 26.172504657 Reorder the terms: -25 + x = 26.172504657 Solving -25 + x = 26.172504657 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 = 26.172504657 + 25 Combine like terms: -25 + 25 = 0 0 + x = 26.172504657 + 25 x = 26.172504657 + 25 Combine like terms: 26.172504657 + 25 = 51.172504657 x = 51.172504657 Simplifying x = 51.172504657Subproblem 2
x + -25 = -26.172504657 Simplifying x + -25 = -26.172504657 Reorder the terms: -25 + x = -26.172504657 Solving -25 + x = -26.172504657 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 = -26.172504657 + 25 Combine like terms: -25 + 25 = 0 0 + x = -26.172504657 + 25 x = -26.172504657 + 25 Combine like terms: -26.172504657 + 25 = -1.172504657 x = -1.172504657 Simplifying x = -1.172504657Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.172504657, -1.172504657}
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