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Simplifying x2 + -50x + 256 = 0 Reorder the terms: 256 + -50x + x2 = 0 Solving 256 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-256' to each side of the equation. 256 + -50x + -256 + x2 = 0 + -256 Reorder the terms: 256 + -256 + -50x + x2 = 0 + -256 Combine like terms: 256 + -256 = 0 0 + -50x + x2 = 0 + -256 -50x + x2 = 0 + -256 Combine like terms: 0 + -256 = -256 -50x + x2 = -256 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 = -256 + 625 Reorder the terms: 625 + -50x + x2 = -256 + 625 Combine like terms: -256 + 625 = 369 625 + -50x + x2 = 369 Factor a perfect square on the left side: (x + -25)(x + -25) = 369 Calculate the square root of the right side: 19.209372712 Break this problem into two subproblems by setting (x + -25) equal to 19.209372712 and -19.209372712.Subproblem 1
x + -25 = 19.209372712 Simplifying x + -25 = 19.209372712 Reorder the terms: -25 + x = 19.209372712 Solving -25 + x = 19.209372712 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 = 19.209372712 + 25 Combine like terms: -25 + 25 = 0 0 + x = 19.209372712 + 25 x = 19.209372712 + 25 Combine like terms: 19.209372712 + 25 = 44.209372712 x = 44.209372712 Simplifying x = 44.209372712Subproblem 2
x + -25 = -19.209372712 Simplifying x + -25 = -19.209372712 Reorder the terms: -25 + x = -19.209372712 Solving -25 + x = -19.209372712 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 = -19.209372712 + 25 Combine like terms: -25 + 25 = 0 0 + x = -19.209372712 + 25 x = -19.209372712 + 25 Combine like terms: -19.209372712 + 25 = 5.790627288 x = 5.790627288 Simplifying x = 5.790627288Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.209372712, 5.790627288}
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