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Simplifying (7 + -1x)(1 + -1x) + -8 = 0 Multiply (7 + -1x) * (1 + -1x) (7(1 + -1x) + -1x * (1 + -1x)) + -8 = 0 ((1 * 7 + -1x * 7) + -1x * (1 + -1x)) + -8 = 0 ((7 + -7x) + -1x * (1 + -1x)) + -8 = 0 (7 + -7x + (1 * -1x + -1x * -1x)) + -8 = 0 (7 + -7x + (-1x + 1x2)) + -8 = 0 Combine like terms: -7x + -1x = -8x (7 + -8x + 1x2) + -8 = 0 Reorder the terms: 7 + -8 + -8x + 1x2 = 0 Combine like terms: 7 + -8 = -1 -1 + -8x + 1x2 = 0 Solving -1 + -8x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8x + x2 = 0 + 1 -8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8x + x2 = 1 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1 + 16 Reorder the terms: 16 + -8x + x2 = 1 + 16 Combine like terms: 1 + 16 = 17 16 + -8x + x2 = 17 Factor a perfect square on the left side: (x + -4)(x + -4) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -4) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -4 = 4.123105626 Simplifying x + -4 = 4.123105626 Reorder the terms: -4 + x = 4.123105626 Solving -4 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.123105626 + 4 x = 4.123105626 + 4 Combine like terms: 4.123105626 + 4 = 8.123105626 x = 8.123105626 Simplifying x = 8.123105626Subproblem 2
x + -4 = -4.123105626 Simplifying x + -4 = -4.123105626 Reorder the terms: -4 + x = -4.123105626 Solving -4 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.123105626 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.123105626 + 4 x = -4.123105626 + 4 Combine like terms: -4.123105626 + 4 = -0.123105626 x = -0.123105626 Simplifying x = -0.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.123105626, -0.123105626}
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