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Simplifying (x + -10)(x + -10) = 2 Reorder the terms: (-10 + x)(x + -10) = 2 Reorder the terms: (-10 + x)(-10 + x) = 2 Multiply (-10 + x) * (-10 + x) (-10(-10 + x) + x(-10 + x)) = 2 ((-10 * -10 + x * -10) + x(-10 + x)) = 2 ((100 + -10x) + x(-10 + x)) = 2 (100 + -10x + (-10 * x + x * x)) = 2 (100 + -10x + (-10x + x2)) = 2 Combine like terms: -10x + -10x = -20x (100 + -20x + x2) = 2 Solving 100 + -20x + x2 = 2 Solving for variable 'x'. Reorder the terms: 100 + -2 + -20x + x2 = 2 + -2 Combine like terms: 100 + -2 = 98 98 + -20x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 98 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-98' to each side of the equation. 98 + -20x + -98 + x2 = 0 + -98 Reorder the terms: 98 + -98 + -20x + x2 = 0 + -98 Combine like terms: 98 + -98 = 0 0 + -20x + x2 = 0 + -98 -20x + x2 = 0 + -98 Combine like terms: 0 + -98 = -98 -20x + x2 = -98 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 = -98 + 100 Reorder the terms: 100 + -20x + x2 = -98 + 100 Combine like terms: -98 + 100 = 2 100 + -20x + x2 = 2 Factor a perfect square on the left side: (x + -10)(x + -10) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -10) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -10 = 1.414213562 Simplifying x + -10 = 1.414213562 Reorder the terms: -10 + x = 1.414213562 Solving -10 + x = 1.414213562 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 = 1.414213562 + 10 Combine like terms: -10 + 10 = 0 0 + x = 1.414213562 + 10 x = 1.414213562 + 10 Combine like terms: 1.414213562 + 10 = 11.414213562 x = 11.414213562 Simplifying x = 11.414213562Subproblem 2
x + -10 = -1.414213562 Simplifying x + -10 = -1.414213562 Reorder the terms: -10 + x = -1.414213562 Solving -10 + x = -1.414213562 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 = -1.414213562 + 10 Combine like terms: -10 + 10 = 0 0 + x = -1.414213562 + 10 x = -1.414213562 + 10 Combine like terms: -1.414213562 + 10 = 8.585786438 x = 8.585786438 Simplifying x = 8.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.414213562, 8.585786438}
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