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Simplifying (8 * 8) + (x + x) = (4 + x)(4 + x) Multiply 8 * 8 (64) + (x + x) = (4 + x)(4 + x) 64 + (x + x) = (4 + x)(4 + x) Combine like terms: x + x = 2x 64 + (2x) = (4 + x)(4 + x) 64 + (2x) = (4 + x)(4 + x) Multiply (4 + x) * (4 + x) 64 + (2x) = (4(4 + x) + x(4 + x)) 64 + (2x) = ((4 * 4 + x * 4) + x(4 + x)) 64 + (2x) = ((16 + 4x) + x(4 + x)) 64 + (2x) = (16 + 4x + (4 * x + x * x)) 64 + (2x) = (16 + 4x + (4x + x2)) Combine like terms: 4x + 4x = 8x 64 + (2x) = (16 + 8x + x2) Solving 64 + (2x) = 16 + 8x + x2 Solving for variable 'x'. Reorder the terms: 64 + -16 + (2x) + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: 64 + -16 = 48 48 + (2x) + -8x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Combine like terms: (2x) + -8x = -6x 48 + -6x + -1x2 = 16 + 8x + x2 + -16 + -8x + -1x2 Reorder the terms: 48 + -6x + -1x2 = 16 + -16 + 8x + -8x + x2 + -1x2 Combine like terms: 16 + -16 = 0 48 + -6x + -1x2 = 0 + 8x + -8x + x2 + -1x2 48 + -6x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 48 + -6x + -1x2 = 0 + x2 + -1x2 48 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + 6x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 6x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 6x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 6x + x2 = 0 + 48 6x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 6x + x2 = 48 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 48 + 9 Reorder the terms: 9 + 6x + x2 = 48 + 9 Combine like terms: 48 + 9 = 57 9 + 6x + x2 = 57 Factor a perfect square on the left side: (x + 3)(x + 3) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 3) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 3 = 7.549834435 Simplifying x + 3 = 7.549834435 Reorder the terms: 3 + x = 7.549834435 Solving 3 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.549834435 + -3 x = 7.549834435 + -3 Combine like terms: 7.549834435 + -3 = 4.549834435 x = 4.549834435 Simplifying x = 4.549834435Subproblem 2
x + 3 = -7.549834435 Simplifying x + 3 = -7.549834435 Reorder the terms: 3 + x = -7.549834435 Solving 3 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.549834435 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.549834435 + -3 x = -7.549834435 + -3 Combine like terms: -7.549834435 + -3 = -10.549834435 x = -10.549834435 Simplifying x = -10.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.549834435, -10.549834435}
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