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Simplifying x2 + 8x + -82 = 6 Reorder the terms: -82 + 8x + x2 = 6 Solving -82 + 8x + x2 = 6 Solving for variable 'x'. Reorder the terms: -82 + -6 + 8x + x2 = 6 + -6 Combine like terms: -82 + -6 = -88 -88 + 8x + x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -88 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 8x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 8x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 8x + x2 = 0 + 88 8x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 8x + x2 = 88 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 = 88 + 16 Reorder the terms: 16 + 8x + x2 = 88 + 16 Combine like terms: 88 + 16 = 104 16 + 8x + x2 = 104 Factor a perfect square on the left side: (x + 4)(x + 4) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (x + 4) equal to 10.198039027 and -10.198039027.Subproblem 1
x + 4 = 10.198039027 Simplifying x + 4 = 10.198039027 Reorder the terms: 4 + x = 10.198039027 Solving 4 + x = 10.198039027 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 = 10.198039027 + -4 Combine like terms: 4 + -4 = 0 0 + x = 10.198039027 + -4 x = 10.198039027 + -4 Combine like terms: 10.198039027 + -4 = 6.198039027 x = 6.198039027 Simplifying x = 6.198039027Subproblem 2
x + 4 = -10.198039027 Simplifying x + 4 = -10.198039027 Reorder the terms: 4 + x = -10.198039027 Solving 4 + x = -10.198039027 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 = -10.198039027 + -4 Combine like terms: 4 + -4 = 0 0 + x = -10.198039027 + -4 x = -10.198039027 + -4 Combine like terms: -10.198039027 + -4 = -14.198039027 x = -14.198039027 Simplifying x = -14.198039027Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.198039027, -14.198039027}
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