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Simplifying (x + 2)(x + 2) + 3x = 0 Reorder the terms: (2 + x)(x + 2) + 3x = 0 Reorder the terms: (2 + x)(2 + x) + 3x = 0 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x)) + 3x = 0 ((2 * 2 + x * 2) + x(2 + x)) + 3x = 0 ((4 + 2x) + x(2 + x)) + 3x = 0 (4 + 2x + (2 * x + x * x)) + 3x = 0 (4 + 2x + (2x + x2)) + 3x = 0 Combine like terms: 2x + 2x = 4x (4 + 4x + x2) + 3x = 0 Reorder the terms: 4 + 4x + 3x + x2 = 0 Combine like terms: 4x + 3x = 7x 4 + 7x + x2 = 0 Solving 4 + 7x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 7x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 7x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 7x + x2 = 0 + -4 7x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 7x + x2 = -4 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -4 + 12.25 Combine like terms: -4 + 12.25 = 8.25 12.25 + 7x + x2 = 8.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 3.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 3.5 = 2.872281323 Simplifying x + 3.5 = 2.872281323 Reorder the terms: 3.5 + x = 2.872281323 Solving 3.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.872281323 + -3.5 x = 2.872281323 + -3.5 Combine like terms: 2.872281323 + -3.5 = -0.627718677 x = -0.627718677 Simplifying x = -0.627718677Subproblem 2
x + 3.5 = -2.872281323 Simplifying x + 3.5 = -2.872281323 Reorder the terms: 3.5 + x = -2.872281323 Solving 3.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.872281323 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.872281323 + -3.5 x = -2.872281323 + -3.5 Combine like terms: -2.872281323 + -3.5 = -6.372281323 x = -6.372281323 Simplifying x = -6.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.627718677, -6.372281323}
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