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Simplifying (x + 5)(x + 5) = 200 Reorder the terms: (5 + x)(x + 5) = 200 Reorder the terms: (5 + x)(5 + x) = 200 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 200 ((5 * 5 + x * 5) + x(5 + x)) = 200 ((25 + 5x) + x(5 + x)) = 200 (25 + 5x + (5 * x + x * x)) = 200 (25 + 5x + (5x + x2)) = 200 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 200 Solving 25 + 10x + x2 = 200 Solving for variable 'x'. Reorder the terms: 25 + -200 + 10x + x2 = 200 + -200 Combine like terms: 25 + -200 = -175 -175 + 10x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -175 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 10x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 10x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 10x + x2 = 0 + 175 10x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 10x + x2 = 175 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 = 175 + 25 Reorder the terms: 25 + 10x + x2 = 175 + 25 Combine like terms: 175 + 25 = 200 25 + 10x + x2 = 200 Factor a perfect square on the left side: (x + 5)(x + 5) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 5) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 5 = 14.142135624 Simplifying x + 5 = 14.142135624 Reorder the terms: 5 + x = 14.142135624 Solving 5 + x = 14.142135624 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 = 14.142135624 + -5 Combine like terms: 5 + -5 = 0 0 + x = 14.142135624 + -5 x = 14.142135624 + -5 Combine like terms: 14.142135624 + -5 = 9.142135624 x = 9.142135624 Simplifying x = 9.142135624Subproblem 2
x + 5 = -14.142135624 Simplifying x + 5 = -14.142135624 Reorder the terms: 5 + x = -14.142135624 Solving 5 + x = -14.142135624 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 = -14.142135624 + -5 Combine like terms: 5 + -5 = 0 0 + x = -14.142135624 + -5 x = -14.142135624 + -5 Combine like terms: -14.142135624 + -5 = -19.142135624 x = -19.142135624 Simplifying x = -19.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.142135624, -19.142135624}
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