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Simplifying (x + 10)(x + 10) = 200 Reorder the terms: (10 + x)(x + 10) = 200 Reorder the terms: (10 + x)(10 + x) = 200 Multiply (10 + x) * (10 + x) (10(10 + x) + x(10 + x)) = 200 ((10 * 10 + x * 10) + x(10 + x)) = 200 ((100 + 10x) + x(10 + x)) = 200 (100 + 10x + (10 * x + x * x)) = 200 (100 + 10x + (10x + x2)) = 200 Combine like terms: 10x + 10x = 20x (100 + 20x + x2) = 200 Solving 100 + 20x + x2 = 200 Solving for variable 'x'. Reorder the terms: 100 + -200 + 20x + x2 = 200 + -200 Combine like terms: 100 + -200 = -100 -100 + 20x + x2 = 200 + -200 Combine like terms: 200 + -200 = 0 -100 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 20x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 20x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 20x + x2 = 0 + 100 20x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 20x + x2 = 100 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 100 + 100 Reorder the terms: 100 + 20x + x2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + 20x + x2 = 200 Factor a perfect square on the left side: (x + 10)(x + 10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + 10) equal to 14.142135624 and -14.142135624.Subproblem 1
x + 10 = 14.142135624 Simplifying x + 10 = 14.142135624 Reorder the terms: 10 + x = 14.142135624 Solving 10 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x = 14.142135624 + -10 x = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 x = 4.142135624 Simplifying x = 4.142135624Subproblem 2
x + 10 = -14.142135624 Simplifying x + 10 = -14.142135624 Reorder the terms: 10 + x = -14.142135624 Solving 10 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + x = -14.142135624 + -10 x = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 x = -24.142135624 Simplifying x = -24.142135624Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.142135624, -24.142135624}
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