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Simplifying x2 + -200x + -284 = 0 Reorder the terms: -284 + -200x + x2 = 0 Solving -284 + -200x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '284' to each side of the equation. -284 + -200x + 284 + x2 = 0 + 284 Reorder the terms: -284 + 284 + -200x + x2 = 0 + 284 Combine like terms: -284 + 284 = 0 0 + -200x + x2 = 0 + 284 -200x + x2 = 0 + 284 Combine like terms: 0 + 284 = 284 -200x + x2 = 284 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 = 284 + 10000 Reorder the terms: 10000 + -200x + x2 = 284 + 10000 Combine like terms: 284 + 10000 = 10284 10000 + -200x + x2 = 10284 Factor a perfect square on the left side: (x + -100)(x + -100) = 10284 Calculate the square root of the right side: 101.410058673 Break this problem into two subproblems by setting (x + -100) equal to 101.410058673 and -101.410058673.Subproblem 1
x + -100 = 101.410058673 Simplifying x + -100 = 101.410058673 Reorder the terms: -100 + x = 101.410058673 Solving -100 + x = 101.410058673 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 = 101.410058673 + 100 Combine like terms: -100 + 100 = 0 0 + x = 101.410058673 + 100 x = 101.410058673 + 100 Combine like terms: 101.410058673 + 100 = 201.410058673 x = 201.410058673 Simplifying x = 201.410058673Subproblem 2
x + -100 = -101.410058673 Simplifying x + -100 = -101.410058673 Reorder the terms: -100 + x = -101.410058673 Solving -100 + x = -101.410058673 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 = -101.410058673 + 100 Combine like terms: -100 + 100 = 0 0 + x = -101.410058673 + 100 x = -101.410058673 + 100 Combine like terms: -101.410058673 + 100 = -1.410058673 x = -1.410058673 Simplifying x = -1.410058673Solution
The solution to the problem is based on the solutions from the subproblems. x = {201.410058673, -1.410058673}
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