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Simplifying (x + 2.5)(x + 2.5) = 0 Reorder the terms: (2.5 + x)(x + 2.5) = 0 Reorder the terms: (2.5 + x)(2.5 + x) = 0 Multiply (2.5 + x) * (2.5 + x) (2.5(2.5 + x) + x(2.5 + x)) = 0 ((2.5 * 2.5 + x * 2.5) + x(2.5 + x)) = 0 ((6.25 + 2.5x) + x(2.5 + x)) = 0 (6.25 + 2.5x + (2.5 * x + x * x)) = 0 (6.25 + 2.5x + (2.5x + x2)) = 0 Combine like terms: 2.5x + 2.5x = 5x (6.25 + 5x + x2) = 0 Solving 6.25 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5x + x2 = 0 + -6.25 5x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5x + x2 = -6.25 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 = -6.25 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -6.25 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 6.25 + 5x + x2 = 0.00 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 2.5) equal to 0.00 and 0.00.Subproblem 1
x + 2.5 = 0.00 Simplifying x + 2.5 = 0.00 Reorder the terms: 2.5 + x = 0.00 Solving 2.5 + x = 0.00 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 = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.00 + -2.5 x = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 2.5 = 0.00 Simplifying x + 2.5 = 0.00 Reorder the terms: 2.5 + x = 0.00 Solving 2.5 + x = 0.00 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 = 0.00 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 0.00 + -2.5 x = 0.00 + -2.5 Combine like terms: 0.00 + -2.5 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -2.5}
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