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Simplifying x = 60x + -1x2 + 18 Reorder the terms: 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 = 888.25 870.25 + -59x + x2 = 888.25 Factor a perfect square on the left side: (x + -29.5)(x + -29.5) = 888.25 Calculate the square root of the right side: 29.803523282 Break this problem into two subproblems by setting (x + -29.5) equal to 29.803523282 and -29.803523282.Subproblem 1
x + -29.5 = 29.803523282 Simplifying x + -29.5 = 29.803523282 Reorder the terms: -29.5 + x = 29.803523282 Solving -29.5 + x = 29.803523282 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 = 29.803523282 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = 29.803523282 + 29.5 x = 29.803523282 + 29.5 Combine like terms: 29.803523282 + 29.5 = 59.303523282 x = 59.303523282 Simplifying x = 59.303523282Subproblem 2
x + -29.5 = -29.803523282 Simplifying x + -29.5 = -29.803523282 Reorder the terms: -29.5 + x = -29.803523282 Solving -29.5 + x = -29.803523282 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 = -29.803523282 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = -29.803523282 + 29.5 x = -29.803523282 + 29.5 Combine like terms: -29.803523282 + 29.5 = -0.303523282 x = -0.303523282 Simplifying x = -0.303523282Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.303523282, -0.303523282}
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