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Simplifying 180 + -1x = x(90 + -1x) 180 + -1x = (90 * x + -1x * x) 180 + -1x = (90x + -1x2) Solving 180 + -1x = 90x + -1x2 Solving for variable 'x'. Combine like terms: -1x + -90x = -91x 180 + -91x + x2 = 90x + -1x2 + -90x + x2 Reorder the terms: 180 + -91x + x2 = 90x + -90x + -1x2 + x2 Combine like terms: 90x + -90x = 0 180 + -91x + x2 = 0 + -1x2 + x2 180 + -91x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 180 + -91x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-180' to each side of the equation. 180 + -91x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -91x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -91x + x2 = 0 + -180 -91x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -91x + x2 = -180 The x term is -91x. Take half its coefficient (-45.5). Square it (2070.25) and add it to both sides. Add '2070.25' to each side of the equation. -91x + 2070.25 + x2 = -180 + 2070.25 Reorder the terms: 2070.25 + -91x + x2 = -180 + 2070.25 Combine like terms: -180 + 2070.25 = 1890.25 2070.25 + -91x + x2 = 1890.25 Factor a perfect square on the left side: (x + -45.5)(x + -45.5) = 1890.25 Calculate the square root of the right side: 43.477005417 Break this problem into two subproblems by setting (x + -45.5) equal to 43.477005417 and -43.477005417.Subproblem 1
x + -45.5 = 43.477005417 Simplifying x + -45.5 = 43.477005417 Reorder the terms: -45.5 + x = 43.477005417 Solving -45.5 + x = 43.477005417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.5' to each side of the equation. -45.5 + 45.5 + x = 43.477005417 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + x = 43.477005417 + 45.5 x = 43.477005417 + 45.5 Combine like terms: 43.477005417 + 45.5 = 88.977005417 x = 88.977005417 Simplifying x = 88.977005417Subproblem 2
x + -45.5 = -43.477005417 Simplifying x + -45.5 = -43.477005417 Reorder the terms: -45.5 + x = -43.477005417 Solving -45.5 + x = -43.477005417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '45.5' to each side of the equation. -45.5 + 45.5 + x = -43.477005417 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + x = -43.477005417 + 45.5 x = -43.477005417 + 45.5 Combine like terms: -43.477005417 + 45.5 = 2.022994583 x = 2.022994583 Simplifying x = 2.022994583Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.977005417, 2.022994583}
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