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Simplifying x = (100x + -1x2) + -1(40x + 18) Remove parenthesis around (100x + -1x2) x = 100x + -1x2 + -1(40x + 18) Reorder the terms: x = 100x + -1x2 + -1(18 + 40x) x = 100x + -1x2 + (18 * -1 + 40x * -1) x = 100x + -1x2 + (-18 + -40x) Reorder the terms: x = -18 + 100x + -40x + -1x2 Combine like terms: 100x + -40x = 60x x = -18 + 60x + -1x2 Solving x = -18 + 60x + -1x2 Solving for variable 'x'. Reorder the terms: 18 + x + -60x + x2 = -18 + 60x + -1x2 + 18 + -60x + x2 Combine like terms: x + -60x = -59x 18 + -59x + x2 = -18 + 60x + -1x2 + 18 + -60x + x2 Reorder the terms: 18 + -59x + x2 = -18 + 18 + 60x + -60x + -1x2 + x2 Combine like terms: -18 + 18 = 0 18 + -59x + x2 = 0 + 60x + -60x + -1x2 + x2 18 + -59x + x2 = 60x + -60x + -1x2 + x2 Combine like terms: 60x + -60x = 0 18 + -59x + x2 = 0 + -1x2 + x2 18 + -59x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 18 + -59x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -59x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -59x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -59x + x2 = 0 + -18 -59x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -59x + x2 = -18 The x term is -59x. Take half its coefficient (-29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. -59x + 870.25 + x2 = -18 + 870.25 Reorder the terms: 870.25 + -59x + x2 = -18 + 870.25 Combine like terms: -18 + 870.25 = 852.25 870.25 + -59x + x2 = 852.25 Factor a perfect square on the left side: (x + -29.5)(x + -29.5) = 852.25 Calculate the square root of the right side: 29.193321154 Break this problem into two subproblems by setting (x + -29.5) equal to 29.193321154 and -29.193321154.Subproblem 1
x + -29.5 = 29.193321154 Simplifying x + -29.5 = 29.193321154 Reorder the terms: -29.5 + x = 29.193321154 Solving -29.5 + x = 29.193321154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = 29.193321154 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = 29.193321154 + 29.5 x = 29.193321154 + 29.5 Combine like terms: 29.193321154 + 29.5 = 58.693321154 x = 58.693321154 Simplifying x = 58.693321154Subproblem 2
x + -29.5 = -29.193321154 Simplifying x + -29.5 = -29.193321154 Reorder the terms: -29.5 + x = -29.193321154 Solving -29.5 + x = -29.193321154 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = -29.193321154 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = -29.193321154 + 29.5 x = -29.193321154 + 29.5 Combine like terms: -29.193321154 + 29.5 = 0.306678846 x = 0.306678846 Simplifying x = 0.306678846Solution
The solution to the problem is based on the solutions from the subproblems. x = {58.693321154, 0.306678846}
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