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Simplifying x2 + -200x + 800 = 0 Reorder the terms: 800 + -200x + x2 = 0 Solving 800 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-800' to each side of the equation. 800 + -200x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -200x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -200x + x2 = 0 + -800 -200x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -200x + x2 = -800 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -800 + 10000 Reorder the terms: 10000 + -200x + x2 = -800 + 10000 Combine like terms: -800 + 10000 = 9200 10000 + -200x + x2 = 9200 Factor a perfect square on the left side: (x + -100)(x + -100) = 9200 Calculate the square root of the right side: 95.916630466 Break this problem into two subproblems by setting (x + -100) equal to 95.916630466 and -95.916630466.Subproblem 1
x + -100 = 95.916630466 Simplifying x + -100 = 95.916630466 Reorder the terms: -100 + x = 95.916630466 Solving -100 + x = 95.916630466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 95.916630466 + 100 Combine like terms: -100 + 100 = 0 0 + x = 95.916630466 + 100 x = 95.916630466 + 100 Combine like terms: 95.916630466 + 100 = 195.916630466 x = 195.916630466 Simplifying x = 195.916630466Subproblem 2
x + -100 = -95.916630466 Simplifying x + -100 = -95.916630466 Reorder the terms: -100 + x = -95.916630466 Solving -100 + x = -95.916630466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -95.916630466 + 100 Combine like terms: -100 + 100 = 0 0 + x = -95.916630466 + 100 x = -95.916630466 + 100 Combine like terms: -95.916630466 + 100 = 4.083369534 x = 4.083369534 Simplifying x = 4.083369534Solution
The solution to the problem is based on the solutions from the subproblems. x = {195.916630466, 4.083369534}
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