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Simplifying x2 + -50x + 222.75 = 0 Reorder the terms: 222.75 + -50x + x2 = 0 Solving 222.75 + -50x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-222.75' to each side of the equation. 222.75 + -50x + -222.75 + x2 = 0 + -222.75 Reorder the terms: 222.75 + -222.75 + -50x + x2 = 0 + -222.75 Combine like terms: 222.75 + -222.75 = 0.00 0.00 + -50x + x2 = 0 + -222.75 -50x + x2 = 0 + -222.75 Combine like terms: 0 + -222.75 = -222.75 -50x + x2 = -222.75 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 = -222.75 + 625 Reorder the terms: 625 + -50x + x2 = -222.75 + 625 Combine like terms: -222.75 + 625 = 402.25 625 + -50x + x2 = 402.25 Factor a perfect square on the left side: (x + -25)(x + -25) = 402.25 Calculate the square root of the right side: 20.05617112 Break this problem into two subproblems by setting (x + -25) equal to 20.05617112 and -20.05617112.Subproblem 1
x + -25 = 20.05617112 Simplifying x + -25 = 20.05617112 Reorder the terms: -25 + x = 20.05617112 Solving -25 + x = 20.05617112 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 = 20.05617112 + 25 Combine like terms: -25 + 25 = 0 0 + x = 20.05617112 + 25 x = 20.05617112 + 25 Combine like terms: 20.05617112 + 25 = 45.05617112 x = 45.05617112 Simplifying x = 45.05617112Subproblem 2
x + -25 = -20.05617112 Simplifying x + -25 = -20.05617112 Reorder the terms: -25 + x = -20.05617112 Solving -25 + x = -20.05617112 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 = -20.05617112 + 25 Combine like terms: -25 + 25 = 0 0 + x = -20.05617112 + 25 x = -20.05617112 + 25 Combine like terms: -20.05617112 + 25 = 4.94382888 x = 4.94382888 Simplifying x = 4.94382888Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.05617112, 4.94382888}
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