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Simplifying x2 + 8x + 10 = 66 Reorder the terms: 10 + 8x + x2 = 66 Solving 10 + 8x + x2 = 66 Solving for variable 'x'. Reorder the terms: 10 + -66 + 8x + x2 = 66 + -66 Combine like terms: 10 + -66 = -56 -56 + 8x + x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -56 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + 8x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 8x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 8x + x2 = 0 + 56 8x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 8x + x2 = 56 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 = 56 + 16 Reorder the terms: 16 + 8x + x2 = 56 + 16 Combine like terms: 56 + 16 = 72 16 + 8x + x2 = 72 Factor a perfect square on the left side: (x + 4)(x + 4) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + 4) equal to 8.485281374 and -8.485281374.Subproblem 1
x + 4 = 8.485281374 Simplifying x + 4 = 8.485281374 Reorder the terms: 4 + x = 8.485281374 Solving 4 + x = 8.485281374 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 = 8.485281374 + -4 Combine like terms: 4 + -4 = 0 0 + x = 8.485281374 + -4 x = 8.485281374 + -4 Combine like terms: 8.485281374 + -4 = 4.485281374 x = 4.485281374 Simplifying x = 4.485281374Subproblem 2
x + 4 = -8.485281374 Simplifying x + 4 = -8.485281374 Reorder the terms: 4 + x = -8.485281374 Solving 4 + x = -8.485281374 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 = -8.485281374 + -4 Combine like terms: 4 + -4 = 0 0 + x = -8.485281374 + -4 x = -8.485281374 + -4 Combine like terms: -8.485281374 + -4 = -12.485281374 x = -12.485281374 Simplifying x = -12.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.485281374, -12.485281374}
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