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Simplifying x2 + -50x + -500 = 0 Reorder the terms: -500 + -50x + x2 = 0 Solving -500 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '500' to each side of the equation. -500 + -50x + 500 + x2 = 0 + 500 Reorder the terms: -500 + 500 + -50x + x2 = 0 + 500 Combine like terms: -500 + 500 = 0 0 + -50x + x2 = 0 + 500 -50x + x2 = 0 + 500 Combine like terms: 0 + 500 = 500 -50x + x2 = 500 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 = 500 + 625 Reorder the terms: 625 + -50x + x2 = 500 + 625 Combine like terms: 500 + 625 = 1125 625 + -50x + x2 = 1125 Factor a perfect square on the left side: (x + -25)(x + -25) = 1125 Calculate the square root of the right side: 33.541019662 Break this problem into two subproblems by setting (x + -25) equal to 33.541019662 and -33.541019662.Subproblem 1
x + -25 = 33.541019662 Simplifying x + -25 = 33.541019662 Reorder the terms: -25 + x = 33.541019662 Solving -25 + x = 33.541019662 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 = 33.541019662 + 25 Combine like terms: -25 + 25 = 0 0 + x = 33.541019662 + 25 x = 33.541019662 + 25 Combine like terms: 33.541019662 + 25 = 58.541019662 x = 58.541019662 Simplifying x = 58.541019662Subproblem 2
x + -25 = -33.541019662 Simplifying x + -25 = -33.541019662 Reorder the terms: -25 + x = -33.541019662 Solving -25 + x = -33.541019662 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 = -33.541019662 + 25 Combine like terms: -25 + 25 = 0 0 + x = -33.541019662 + 25 x = -33.541019662 + 25 Combine like terms: -33.541019662 + 25 = -8.541019662 x = -8.541019662 Simplifying x = -8.541019662Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.541019662, -8.541019662}
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