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Simplifying x2 + -8x + -29 = 0 Reorder the terms: -29 + -8x + x2 = 0 Solving -29 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -8x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -8x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -8x + x2 = 0 + 29 -8x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -8x + x2 = 29 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 = 29 + 16 Reorder the terms: 16 + -8x + x2 = 29 + 16 Combine like terms: 29 + 16 = 45 16 + -8x + x2 = 45 Factor a perfect square on the left side: (x + -4)(x + -4) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -4) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -4 = 6.708203933 Simplifying x + -4 = 6.708203933 Reorder the terms: -4 + x = 6.708203933 Solving -4 + x = 6.708203933 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 = 6.708203933 + 4 Combine like terms: -4 + 4 = 0 0 + x = 6.708203933 + 4 x = 6.708203933 + 4 Combine like terms: 6.708203933 + 4 = 10.708203933 x = 10.708203933 Simplifying x = 10.708203933Subproblem 2
x + -4 = -6.708203933 Simplifying x + -4 = -6.708203933 Reorder the terms: -4 + x = -6.708203933 Solving -4 + x = -6.708203933 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 = -6.708203933 + 4 Combine like terms: -4 + 4 = 0 0 + x = -6.708203933 + 4 x = -6.708203933 + 4 Combine like terms: -6.708203933 + 4 = -2.708203933 x = -2.708203933 Simplifying x = -2.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.708203933, -2.708203933}
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