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Simplifying x2 + -400x + 3600 = 0 Reorder the terms: 3600 + -400x + x2 = 0 Solving 3600 + -400x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3600' to each side of the equation. 3600 + -400x + -3600 + x2 = 0 + -3600 Reorder the terms: 3600 + -3600 + -400x + x2 = 0 + -3600 Combine like terms: 3600 + -3600 = 0 0 + -400x + x2 = 0 + -3600 -400x + x2 = 0 + -3600 Combine like terms: 0 + -3600 = -3600 -400x + x2 = -3600 The x term is -400x. Take half its coefficient (-200). Square it (40000) and add it to both sides. Add '40000' to each side of the equation. -400x + 40000 + x2 = -3600 + 40000 Reorder the terms: 40000 + -400x + x2 = -3600 + 40000 Combine like terms: -3600 + 40000 = 36400 40000 + -400x + x2 = 36400 Factor a perfect square on the left side: (x + -200)(x + -200) = 36400 Calculate the square root of the right side: 190.787840283 Break this problem into two subproblems by setting (x + -200) equal to 190.787840283 and -190.787840283.Subproblem 1
x + -200 = 190.787840283 Simplifying x + -200 = 190.787840283 Reorder the terms: -200 + x = 190.787840283 Solving -200 + x = 190.787840283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 190.787840283 + 200 Combine like terms: -200 + 200 = 0 0 + x = 190.787840283 + 200 x = 190.787840283 + 200 Combine like terms: 190.787840283 + 200 = 390.787840283 x = 390.787840283 Simplifying x = 390.787840283Subproblem 2
x + -200 = -190.787840283 Simplifying x + -200 = -190.787840283 Reorder the terms: -200 + x = -190.787840283 Solving -200 + x = -190.787840283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -190.787840283 + 200 Combine like terms: -200 + 200 = 0 0 + x = -190.787840283 + 200 x = -190.787840283 + 200 Combine like terms: -190.787840283 + 200 = 9.212159717 x = 9.212159717 Simplifying x = 9.212159717Solution
The solution to the problem is based on the solutions from the subproblems. x = {390.787840283, 9.212159717}
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