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Simplifying x2 + (x + 2) = 340 Reorder the terms: x2 + (2 + x) = 340 Remove parenthesis around (2 + x) x2 + 2 + x = 340 Reorder the terms: 2 + x + x2 = 340 Solving 2 + x + x2 = 340 Solving for variable 'x'. Reorder the terms: 2 + -340 + x + x2 = 340 + -340 Combine like terms: 2 + -340 = -338 -338 + x + x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -338 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '338' to each side of the equation. -338 + x + 338 + x2 = 0 + 338 Reorder the terms: -338 + 338 + x + x2 = 0 + 338 Combine like terms: -338 + 338 = 0 0 + x + x2 = 0 + 338 x + x2 = 0 + 338 Combine like terms: 0 + 338 = 338 x + x2 = 338 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 = 338 + 0.25 Reorder the terms: 0.25 + x + x2 = 338 + 0.25 Combine like terms: 338 + 0.25 = 338.25 0.25 + x + x2 = 338.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 338.25 Calculate the square root of the right side: 18.391574158 Break this problem into two subproblems by setting (x + 0.5) equal to 18.391574158 and -18.391574158.Subproblem 1
x + 0.5 = 18.391574158 Simplifying x + 0.5 = 18.391574158 Reorder the terms: 0.5 + x = 18.391574158 Solving 0.5 + x = 18.391574158 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 = 18.391574158 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.391574158 + -0.5 x = 18.391574158 + -0.5 Combine like terms: 18.391574158 + -0.5 = 17.891574158 x = 17.891574158 Simplifying x = 17.891574158Subproblem 2
x + 0.5 = -18.391574158 Simplifying x + 0.5 = -18.391574158 Reorder the terms: 0.5 + x = -18.391574158 Solving 0.5 + x = -18.391574158 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 = -18.391574158 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.391574158 + -0.5 x = -18.391574158 + -0.5 Combine like terms: -18.391574158 + -0.5 = -18.891574158 x = -18.891574158 Simplifying x = -18.891574158Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.891574158, -18.891574158}
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