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Simplifying x2 + -45x = 200 Reorder the terms: -45x + x2 = 200 Solving -45x + x2 = 200 Solving for variable 'x'. Reorder the terms: -200 + -45x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + -45x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -45x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -45x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -45x + x2 = 0 + 200 -45x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -45x + x2 = 200 The x term is -45x. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45x + 506.25 + x2 = 200 + 506.25 Reorder the terms: 506.25 + -45x + x2 = 200 + 506.25 Combine like terms: 200 + 506.25 = 706.25 506.25 + -45x + x2 = 706.25 Factor a perfect square on the left side: (x + -22.5)(x + -22.5) = 706.25 Calculate the square root of the right side: 26.575364532 Break this problem into two subproblems by setting (x + -22.5) equal to 26.575364532 and -26.575364532.Subproblem 1
x + -22.5 = 26.575364532 Simplifying x + -22.5 = 26.575364532 Reorder the terms: -22.5 + x = 26.575364532 Solving -22.5 + x = 26.575364532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = 26.575364532 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = 26.575364532 + 22.5 x = 26.575364532 + 22.5 Combine like terms: 26.575364532 + 22.5 = 49.075364532 x = 49.075364532 Simplifying x = 49.075364532Subproblem 2
x + -22.5 = -26.575364532 Simplifying x + -22.5 = -26.575364532 Reorder the terms: -22.5 + x = -26.575364532 Solving -22.5 + x = -26.575364532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + x = -26.575364532 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + x = -26.575364532 + 22.5 x = -26.575364532 + 22.5 Combine like terms: -26.575364532 + 22.5 = -4.075364532 x = -4.075364532 Simplifying x = -4.075364532Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.075364532, -4.075364532}
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