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Simplifying x2 + -20x = 200 Reorder the terms: -20x + x2 = 200 Solving -20x + x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -20x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -20x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -20x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -20x + x2 = 0 + 200 -20x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -20x + x2 = 200 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 200 + 100 Reorder the terms: 100 + -20x + x2 = 200 + 100 Combine like terms: 200 + 100 = 300 100 + -20x + x2 = 300 Factor a perfect square on the left side: (x + -10)(x + -10) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + -10) equal to 17.320508076 and -17.320508076.Subproblem 1
x + -10 = 17.320508076 Simplifying x + -10 = 17.320508076 Reorder the terms: -10 + x = 17.320508076 Solving -10 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 17.320508076 + 10 Combine like terms: -10 + 10 = 0 0 + x = 17.320508076 + 10 x = 17.320508076 + 10 Combine like terms: 17.320508076 + 10 = 27.320508076 x = 27.320508076 Simplifying x = 27.320508076Subproblem 2
x + -10 = -17.320508076 Simplifying x + -10 = -17.320508076 Reorder the terms: -10 + x = -17.320508076 Solving -10 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -17.320508076 + 10 Combine like terms: -10 + 10 = 0 0 + x = -17.320508076 + 10 x = -17.320508076 + 10 Combine like terms: -17.320508076 + 10 = -7.320508076 x = -7.320508076 Simplifying x = -7.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.320508076, -7.320508076}
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