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Simplifying (x + 5)(x + 5) = 75 Reorder the terms: (5 + x)(x + 5) = 75 Reorder the terms: (5 + x)(5 + x) = 75 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 75 ((5 * 5 + x * 5) + x(5 + x)) = 75 ((25 + 5x) + x(5 + x)) = 75 (25 + 5x + (5 * x + x * x)) = 75 (25 + 5x + (5x + x2)) = 75 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 75 Solving 25 + 10x + x2 = 75 Solving for variable 'x'. Reorder the terms: 25 + -75 + 10x + x2 = 75 + -75 Combine like terms: 25 + -75 = -50 -50 + 10x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -50 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 10x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 10x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 10x + x2 = 0 + 50 10x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 10x + x2 = 50 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 = 50 + 25 Reorder the terms: 25 + 10x + x2 = 50 + 25 Combine like terms: 50 + 25 = 75 25 + 10x + x2 = 75 Factor a perfect square on the left side: (x + 5)(x + 5) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + 5) equal to 8.660254038 and -8.660254038.Subproblem 1
x + 5 = 8.660254038 Simplifying x + 5 = 8.660254038 Reorder the terms: 5 + x = 8.660254038 Solving 5 + x = 8.660254038 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 = 8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + x = 8.660254038 + -5 x = 8.660254038 + -5 Combine like terms: 8.660254038 + -5 = 3.660254038 x = 3.660254038 Simplifying x = 3.660254038Subproblem 2
x + 5 = -8.660254038 Simplifying x + 5 = -8.660254038 Reorder the terms: 5 + x = -8.660254038 Solving 5 + x = -8.660254038 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 = -8.660254038 + -5 Combine like terms: 5 + -5 = 0 0 + x = -8.660254038 + -5 x = -8.660254038 + -5 Combine like terms: -8.660254038 + -5 = -13.660254038 x = -13.660254038 Simplifying x = -13.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.660254038, -13.660254038}
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