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Simplifying (90 + -1x) + ((90 + -1x)(90 + -1x)) + -180 = 0 Remove parenthesis around (90 + -1x) 90 + -1x + ((90 + -1x)(90 + -1x)) + -180 = 0 Multiply (90 + -1x) * (90 + -1x) 90 + -1x + ((90(90 + -1x) + -1x * (90 + -1x))) + -180 = 0 90 + -1x + (((90 * 90 + -1x * 90) + -1x * (90 + -1x))) + -180 = 0 90 + -1x + (((8100 + -90x) + -1x * (90 + -1x))) + -180 = 0 90 + -1x + ((8100 + -90x + (90 * -1x + -1x * -1x))) + -180 = 0 90 + -1x + ((8100 + -90x + (-90x + 1x2))) + -180 = 0 Combine like terms: -90x + -90x = -180x 90 + -1x + ((8100 + -180x + 1x2)) + -180 = 0 90 + -1x + (8100 + -180x + 1x2) + -180 = 0 Remove parenthesis around (8100 + -180x + 1x2) 90 + -1x + 8100 + -180x + 1x2 + -180 = 0 Reorder the terms: 90 + 8100 + -180 + -1x + -180x + 1x2 = 0 Combine like terms: 90 + 8100 = 8190 8190 + -180 + -1x + -180x + 1x2 = 0 Combine like terms: 8190 + -180 = 8010 8010 + -1x + -180x + 1x2 = 0 Combine like terms: -1x + -180x = -181x 8010 + -181x + 1x2 = 0 Solving 8010 + -181x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-8010' to each side of the equation. 8010 + -181x + -8010 + x2 = 0 + -8010 Reorder the terms: 8010 + -8010 + -181x + x2 = 0 + -8010 Combine like terms: 8010 + -8010 = 0 0 + -181x + x2 = 0 + -8010 -181x + x2 = 0 + -8010 Combine like terms: 0 + -8010 = -8010 -181x + x2 = -8010 The x term is -181x. Take half its coefficient (-90.5). Square it (8190.25) and add it to both sides. Add '8190.25' to each side of the equation. -181x + 8190.25 + x2 = -8010 + 8190.25 Reorder the terms: 8190.25 + -181x + x2 = -8010 + 8190.25 Combine like terms: -8010 + 8190.25 = 180.25 8190.25 + -181x + x2 = 180.25 Factor a perfect square on the left side: (x + -90.5)(x + -90.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -90.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -90.5 = 13.425721582 Simplifying x + -90.5 = 13.425721582 Reorder the terms: -90.5 + x = 13.425721582 Solving -90.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.5' to each side of the equation. -90.5 + 90.5 + x = 13.425721582 + 90.5 Combine like terms: -90.5 + 90.5 = 0.0 0.0 + x = 13.425721582 + 90.5 x = 13.425721582 + 90.5 Combine like terms: 13.425721582 + 90.5 = 103.925721582 x = 103.925721582 Simplifying x = 103.925721582Subproblem 2
x + -90.5 = -13.425721582 Simplifying x + -90.5 = -13.425721582 Reorder the terms: -90.5 + x = -13.425721582 Solving -90.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90.5' to each side of the equation. -90.5 + 90.5 + x = -13.425721582 + 90.5 Combine like terms: -90.5 + 90.5 = 0.0 0.0 + x = -13.425721582 + 90.5 x = -13.425721582 + 90.5 Combine like terms: -13.425721582 + 90.5 = 77.074278418 x = 77.074278418 Simplifying x = 77.074278418Solution
The solution to the problem is based on the solutions from the subproblems. x = {103.925721582, 77.074278418}
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