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Simplifying x2 + 360x = 100 Reorder the terms: 360x + x2 = 100 Solving 360x + x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 360x + x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 360x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 360x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 360x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 360x + x2 = 0 + 100 360x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 360x + x2 = 100 The x term is 360x. Take half its coefficient (180). Square it (32400) and add it to both sides. Add '32400' to each side of the equation. 360x + 32400 + x2 = 100 + 32400 Reorder the terms: 32400 + 360x + x2 = 100 + 32400 Combine like terms: 100 + 32400 = 32500 32400 + 360x + x2 = 32500 Factor a perfect square on the left side: (x + 180)(x + 180) = 32500 Calculate the square root of the right side: 180.277563773 Break this problem into two subproblems by setting (x + 180) equal to 180.277563773 and -180.277563773.Subproblem 1
x + 180 = 180.277563773 Simplifying x + 180 = 180.277563773 Reorder the terms: 180 + x = 180.277563773 Solving 180 + x = 180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + x = 180.277563773 + -180 Combine like terms: 180 + -180 = 0 0 + x = 180.277563773 + -180 x = 180.277563773 + -180 Combine like terms: 180.277563773 + -180 = 0.277563773 x = 0.277563773 Simplifying x = 0.277563773Subproblem 2
x + 180 = -180.277563773 Simplifying x + 180 = -180.277563773 Reorder the terms: 180 + x = -180.277563773 Solving 180 + x = -180.277563773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-180' to each side of the equation. 180 + -180 + x = -180.277563773 + -180 Combine like terms: 180 + -180 = 0 0 + x = -180.277563773 + -180 x = -180.277563773 + -180 Combine like terms: -180.277563773 + -180 = -360.277563773 x = -360.277563773 Simplifying x = -360.277563773Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.277563773, -360.277563773}
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