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Simplifying X + X2 = 2.69 Solving X + X2 = 2.69 Solving for variable 'X'. Reorder the terms: -2.69 + X + X2 = 2.69 + -2.69 Combine like terms: 2.69 + -2.69 = 0.00 -2.69 + X + X2 = 0.00 Begin completing the square. Move the constant term to the right: Add '2.69' to each side of the equation. -2.69 + X + 2.69 + X2 = 0.00 + 2.69 Reorder the terms: -2.69 + 2.69 + X + X2 = 0.00 + 2.69 Combine like terms: -2.69 + 2.69 = 0.00 0.00 + X + X2 = 0.00 + 2.69 X + X2 = 0.00 + 2.69 Combine like terms: 0.00 + 2.69 = 2.69 X + X2 = 2.69 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 = 2.69 + 0.25 Reorder the terms: 0.25 + X + X2 = 2.69 + 0.25 Combine like terms: 2.69 + 0.25 = 2.94 0.25 + X + X2 = 2.94 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 2.94 Calculate the square root of the right side: 1.71464282 Break this problem into two subproblems by setting (X + 0.5) equal to 1.71464282 and -1.71464282.Subproblem 1
X + 0.5 = 1.71464282 Simplifying X + 0.5 = 1.71464282 Reorder the terms: 0.5 + X = 1.71464282 Solving 0.5 + X = 1.71464282 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 = 1.71464282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.71464282 + -0.5 X = 1.71464282 + -0.5 Combine like terms: 1.71464282 + -0.5 = 1.21464282 X = 1.21464282 Simplifying X = 1.21464282Subproblem 2
X + 0.5 = -1.71464282 Simplifying X + 0.5 = -1.71464282 Reorder the terms: 0.5 + X = -1.71464282 Solving 0.5 + X = -1.71464282 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 = -1.71464282 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.71464282 + -0.5 X = -1.71464282 + -0.5 Combine like terms: -1.71464282 + -0.5 = -2.21464282 X = -2.21464282 Simplifying X = -2.21464282Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.21464282, -2.21464282}
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