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Simplifying x2 + 3x + 2 = 45 Reorder the terms: 2 + 3x + x2 = 45 Solving 2 + 3x + x2 = 45 Solving for variable 'x'. Reorder the terms: 2 + -45 + 3x + x2 = 45 + -45 Combine like terms: 2 + -45 = -43 -43 + 3x + x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -43 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 3x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 3x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 3x + x2 = 0 + 43 3x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 3x + x2 = 43 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 = 43 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 43 + 2.25 Combine like terms: 43 + 2.25 = 45.25 2.25 + 3x + x2 = 45.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 1.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 1.5 = 6.726812024 Simplifying x + 1.5 = 6.726812024 Reorder the terms: 1.5 + x = 6.726812024 Solving 1.5 + x = 6.726812024 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 = 6.726812024 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.726812024 + -1.5 x = 6.726812024 + -1.5 Combine like terms: 6.726812024 + -1.5 = 5.226812024 x = 5.226812024 Simplifying x = 5.226812024Subproblem 2
x + 1.5 = -6.726812024 Simplifying x + 1.5 = -6.726812024 Reorder the terms: 1.5 + x = -6.726812024 Solving 1.5 + x = -6.726812024 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 = -6.726812024 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.726812024 + -1.5 x = -6.726812024 + -1.5 Combine like terms: -6.726812024 + -1.5 = -8.226812024 x = -8.226812024 Simplifying x = -8.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.226812024, -8.226812024}
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