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Simplifying (8 + x)(6 + x) = 96 Multiply (8 + x) * (6 + x) (8(6 + x) + x(6 + x)) = 96 ((6 * 8 + x * 8) + x(6 + x)) = 96 ((48 + 8x) + x(6 + x)) = 96 (48 + 8x + (6 * x + x * x)) = 96 (48 + 8x + (6x + x2)) = 96 Combine like terms: 8x + 6x = 14x (48 + 14x + x2) = 96 Solving 48 + 14x + x2 = 96 Solving for variable 'x'. Reorder the terms: 48 + -96 + 14x + x2 = 96 + -96 Combine like terms: 48 + -96 = -48 -48 + 14x + x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -48 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 14x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 14x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 14x + x2 = 0 + 48 14x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 14x + x2 = 48 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 48 + 49 Reorder the terms: 49 + 14x + x2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + 14x + x2 = 97 Factor a perfect square on the left side: (x + 7)(x + 7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 7) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 7 = 9.848857802 Simplifying x + 7 = 9.848857802 Reorder the terms: 7 + x = 9.848857802 Solving 7 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + x = 9.848857802 + -7 x = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 x = 2.848857802 Simplifying x = 2.848857802Subproblem 2
x + 7 = -9.848857802 Simplifying x + 7 = -9.848857802 Reorder the terms: 7 + x = -9.848857802 Solving 7 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + x = -9.848857802 + -7 x = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 x = -16.848857802 Simplifying x = -16.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.848857802, -16.848857802}
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