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Simplifying 45 * 180 + -244x + x2 = 0 Multiply 45 * 180 8100 + -244x + x2 = 0 Solving 8100 + -244x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8100' to each side of the equation. 8100 + -244x + -8100 + x2 = 0 + -8100 Reorder the terms: 8100 + -8100 + -244x + x2 = 0 + -8100 Combine like terms: 8100 + -8100 = 0 0 + -244x + x2 = 0 + -8100 -244x + x2 = 0 + -8100 Combine like terms: 0 + -8100 = -8100 -244x + x2 = -8100 The x term is -244x. Take half its coefficient (-122). Square it (14884) and add it to both sides. Add '14884' to each side of the equation. -244x + 14884 + x2 = -8100 + 14884 Reorder the terms: 14884 + -244x + x2 = -8100 + 14884 Combine like terms: -8100 + 14884 = 6784 14884 + -244x + x2 = 6784 Factor a perfect square on the left side: (x + -122)(x + -122) = 6784 Calculate the square root of the right side: 82.365041128 Break this problem into two subproblems by setting (x + -122) equal to 82.365041128 and -82.365041128.Subproblem 1
x + -122 = 82.365041128 Simplifying x + -122 = 82.365041128 Reorder the terms: -122 + x = 82.365041128 Solving -122 + x = 82.365041128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '122' to each side of the equation. -122 + 122 + x = 82.365041128 + 122 Combine like terms: -122 + 122 = 0 0 + x = 82.365041128 + 122 x = 82.365041128 + 122 Combine like terms: 82.365041128 + 122 = 204.365041128 x = 204.365041128 Simplifying x = 204.365041128Subproblem 2
x + -122 = -82.365041128 Simplifying x + -122 = -82.365041128 Reorder the terms: -122 + x = -82.365041128 Solving -122 + x = -82.365041128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '122' to each side of the equation. -122 + 122 + x = -82.365041128 + 122 Combine like terms: -122 + 122 = 0 0 + x = -82.365041128 + 122 x = -82.365041128 + 122 Combine like terms: -82.365041128 + 122 = 39.634958872 x = 39.634958872 Simplifying x = 39.634958872Solution
The solution to the problem is based on the solutions from the subproblems. x = {204.365041128, 39.634958872}
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