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Simplifying x2 + x = 3.55555556 Reorder the terms: x + x2 = 3.55555556 Solving x + x2 = 3.55555556 Solving for variable 'x'. Reorder the terms: -3.55555556 + x + x2 = 3.55555556 + -3.55555556 Combine like terms: 3.55555556 + -3.55555556 = 0.00000000 -3.55555556 + x + x2 = 0.00000000 Begin completing the square. Move the constant term to the right: Add '3.55555556' to each side of the equation. -3.55555556 + x + 3.55555556 + x2 = 0.00000000 + 3.55555556 Reorder the terms: -3.55555556 + 3.55555556 + x + x2 = 0.00000000 + 3.55555556 Combine like terms: -3.55555556 + 3.55555556 = 0.00000000 0.00000000 + x + x2 = 0.00000000 + 3.55555556 x + x2 = 0.00000000 + 3.55555556 Combine like terms: 0.00000000 + 3.55555556 = 3.55555556 x + x2 = 3.55555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3.55555556 + 0.25 Reorder the terms: 0.25 + x + x2 = 3.55555556 + 0.25 Combine like terms: 3.55555556 + 0.25 = 3.80555556 0.25 + x + x2 = 3.80555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.80555556 Calculate the square root of the right side: 1.95078332 Break this problem into two subproblems by setting (x + 0.5) equal to 1.95078332 and -1.95078332.Subproblem 1
x + 0.5 = 1.95078332 Simplifying x + 0.5 = 1.95078332 Reorder the terms: 0.5 + x = 1.95078332 Solving 0.5 + x = 1.95078332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.95078332 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.95078332 + -0.5 x = 1.95078332 + -0.5 Combine like terms: 1.95078332 + -0.5 = 1.45078332 x = 1.45078332 Simplifying x = 1.45078332Subproblem 2
x + 0.5 = -1.95078332 Simplifying x + 0.5 = -1.95078332 Reorder the terms: 0.5 + x = -1.95078332 Solving 0.5 + x = -1.95078332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.95078332 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.95078332 + -0.5 x = -1.95078332 + -0.5 Combine like terms: -1.95078332 + -0.5 = -2.45078332 x = -2.45078332 Simplifying x = -2.45078332Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.45078332, -2.45078332}
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