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Simplifying (x + 5)(x + 5) = 275 Reorder the terms: (5 + x)(x + 5) = 275 Reorder the terms: (5 + x)(5 + x) = 275 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 275 ((5 * 5 + x * 5) + x(5 + x)) = 275 ((25 + 5x) + x(5 + x)) = 275 (25 + 5x + (5 * x + x * x)) = 275 (25 + 5x + (5x + x2)) = 275 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 275 Solving 25 + 10x + x2 = 275 Solving for variable 'x'. Reorder the terms: 25 + -275 + 10x + x2 = 275 + -275 Combine like terms: 25 + -275 = -250 -250 + 10x + x2 = 275 + -275 Combine like terms: 275 + -275 = 0 -250 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '250' to each side of the equation. -250 + 10x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + 10x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + 10x + x2 = 0 + 250 10x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 10x + x2 = 250 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 250 + 25 Reorder the terms: 25 + 10x + x2 = 250 + 25 Combine like terms: 250 + 25 = 275 25 + 10x + x2 = 275 Factor a perfect square on the left side: (x + 5)(x + 5) = 275 Calculate the square root of the right side: 16.583123952 Break this problem into two subproblems by setting (x + 5) equal to 16.583123952 and -16.583123952.Subproblem 1
x + 5 = 16.583123952 Simplifying x + 5 = 16.583123952 Reorder the terms: 5 + x = 16.583123952 Solving 5 + x = 16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 16.583123952 + -5 Combine like terms: 5 + -5 = 0 0 + x = 16.583123952 + -5 x = 16.583123952 + -5 Combine like terms: 16.583123952 + -5 = 11.583123952 x = 11.583123952 Simplifying x = 11.583123952Subproblem 2
x + 5 = -16.583123952 Simplifying x + 5 = -16.583123952 Reorder the terms: 5 + x = -16.583123952 Solving 5 + x = -16.583123952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -16.583123952 + -5 Combine like terms: 5 + -5 = 0 0 + x = -16.583123952 + -5 x = -16.583123952 + -5 Combine like terms: -16.583123952 + -5 = -21.583123952 x = -21.583123952 Simplifying x = -21.583123952Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.583123952, -21.583123952}
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