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Simplifying 1 + 1 + x + 1 + 2x + x2 = 3.1156 Reorder the terms: 1 + 1 + 1 + x + 2x + x2 = 3.1156 Combine like terms: 1 + 1 = 2 2 + 1 + x + 2x + x2 = 3.1156 Combine like terms: 2 + 1 = 3 3 + x + 2x + x2 = 3.1156 Combine like terms: x + 2x = 3x 3 + 3x + x2 = 3.1156 Solving 3 + 3x + x2 = 3.1156 Solving for variable 'x'. Reorder the terms: 3 + -3.1156 + 3x + x2 = 3.1156 + -3.1156 Combine like terms: 3 + -3.1156 = -0.1156 -0.1156 + 3x + x2 = 3.1156 + -3.1156 Combine like terms: 3.1156 + -3.1156 = 0.0000 -0.1156 + 3x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.1156' to each side of the equation. -0.1156 + 3x + 0.1156 + x2 = 0.0000 + 0.1156 Reorder the terms: -0.1156 + 0.1156 + 3x + x2 = 0.0000 + 0.1156 Combine like terms: -0.1156 + 0.1156 = 0.0000 0.0000 + 3x + x2 = 0.0000 + 0.1156 3x + x2 = 0.0000 + 0.1156 Combine like terms: 0.0000 + 0.1156 = 0.1156 3x + x2 = 0.1156 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 0.1156 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.1156 + 2.25 Combine like terms: 0.1156 + 2.25 = 2.3656 2.25 + 3x + x2 = 2.3656 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2.3656 Calculate the square root of the right side: 1.538050714 Break this problem into two subproblems by setting (x + 1.5) equal to 1.538050714 and -1.538050714.Subproblem 1
x + 1.5 = 1.538050714 Simplifying x + 1.5 = 1.538050714 Reorder the terms: 1.5 + x = 1.538050714 Solving 1.5 + x = 1.538050714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.538050714 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.538050714 + -1.5 x = 1.538050714 + -1.5 Combine like terms: 1.538050714 + -1.5 = 0.038050714 x = 0.038050714 Simplifying x = 0.038050714Subproblem 2
x + 1.5 = -1.538050714 Simplifying x + 1.5 = -1.538050714 Reorder the terms: 1.5 + x = -1.538050714 Solving 1.5 + x = -1.538050714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.538050714 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.538050714 + -1.5 x = -1.538050714 + -1.5 Combine like terms: -1.538050714 + -1.5 = -3.038050714 x = -3.038050714 Simplifying x = -3.038050714Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038050714, -3.038050714}
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