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Simplifying 2(x2 + 4x + 3) + -1(x2 + 3x + 1) = 0 Reorder the terms: 2(3 + 4x + x2) + -1(x2 + 3x + 1) = 0 (3 * 2 + 4x * 2 + x2 * 2) + -1(x2 + 3x + 1) = 0 (6 + 8x + 2x2) + -1(x2 + 3x + 1) = 0 Reorder the terms: 6 + 8x + 2x2 + -1(1 + 3x + x2) = 0 6 + 8x + 2x2 + (1 * -1 + 3x * -1 + x2 * -1) = 0 6 + 8x + 2x2 + (-1 + -3x + -1x2) = 0 Reorder the terms: 6 + -1 + 8x + -3x + 2x2 + -1x2 = 0 Combine like terms: 6 + -1 = 5 5 + 8x + -3x + 2x2 + -1x2 = 0 Combine like terms: 8x + -3x = 5x 5 + 5x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 5 + 5x + 1x2 = 0 Solving 5 + 5x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5x + x2 = 0 + -5 5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 5x + x2 = -5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + 5x + x2 = 1.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 2.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + 2.5 = 1.118033989 Simplifying x + 2.5 = 1.118033989 Reorder the terms: 2.5 + x = 1.118033989 Solving 2.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.118033989 + -2.5 x = 1.118033989 + -2.5 Combine like terms: 1.118033989 + -2.5 = -1.381966011 x = -1.381966011 Simplifying x = -1.381966011Subproblem 2
x + 2.5 = -1.118033989 Simplifying x + 2.5 = -1.118033989 Reorder the terms: 2.5 + x = -1.118033989 Solving 2.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.118033989 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.118033989 + -2.5 x = -1.118033989 + -2.5 Combine like terms: -1.118033989 + -2.5 = -3.618033989 x = -3.618033989 Simplifying x = -3.618033989Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.381966011, -3.618033989}
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