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Simplifying (x + -8)(x + -10) = 1 Reorder the terms: (-8 + x)(x + -10) = 1 Reorder the terms: (-8 + x)(-10 + x) = 1 Multiply (-8 + x) * (-10 + x) (-8(-10 + x) + x(-10 + x)) = 1 ((-10 * -8 + x * -8) + x(-10 + x)) = 1 ((80 + -8x) + x(-10 + x)) = 1 (80 + -8x + (-10 * x + x * x)) = 1 (80 + -8x + (-10x + x2)) = 1 Combine like terms: -8x + -10x = -18x (80 + -18x + x2) = 1 Solving 80 + -18x + x2 = 1 Solving for variable 'x'. Reorder the terms: 80 + -1 + -18x + x2 = 1 + -1 Combine like terms: 80 + -1 = 79 79 + -18x + x2 = 1 + -1 Combine like terms: 1 + -1 = 0 79 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-79' to each side of the equation. 79 + -18x + -79 + x2 = 0 + -79 Reorder the terms: 79 + -79 + -18x + x2 = 0 + -79 Combine like terms: 79 + -79 = 0 0 + -18x + x2 = 0 + -79 -18x + x2 = 0 + -79 Combine like terms: 0 + -79 = -79 -18x + x2 = -79 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -79 + 81 Reorder the terms: 81 + -18x + x2 = -79 + 81 Combine like terms: -79 + 81 = 2 81 + -18x + x2 = 2 Factor a perfect square on the left side: (x + -9)(x + -9) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -9) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -9 = 1.414213562 Simplifying x + -9 = 1.414213562 Reorder the terms: -9 + x = 1.414213562 Solving -9 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 1.414213562 + 9 Combine like terms: -9 + 9 = 0 0 + x = 1.414213562 + 9 x = 1.414213562 + 9 Combine like terms: 1.414213562 + 9 = 10.414213562 x = 10.414213562 Simplifying x = 10.414213562Subproblem 2
x + -9 = -1.414213562 Simplifying x + -9 = -1.414213562 Reorder the terms: -9 + x = -1.414213562 Solving -9 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -1.414213562 + 9 Combine like terms: -9 + 9 = 0 0 + x = -1.414213562 + 9 x = -1.414213562 + 9 Combine like terms: -1.414213562 + 9 = 7.585786438 x = 7.585786438 Simplifying x = 7.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.414213562, 7.585786438}
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