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Simplifying (x + 6)(x + 9) = 3263 Reorder the terms: (6 + x)(x + 9) = 3263 Reorder the terms: (6 + x)(9 + x) = 3263 Multiply (6 + x) * (9 + x) (6(9 + x) + x(9 + x)) = 3263 ((9 * 6 + x * 6) + x(9 + x)) = 3263 ((54 + 6x) + x(9 + x)) = 3263 (54 + 6x + (9 * x + x * x)) = 3263 (54 + 6x + (9x + x2)) = 3263 Combine like terms: 6x + 9x = 15x (54 + 15x + x2) = 3263 Solving 54 + 15x + x2 = 3263 Solving for variable 'x'. Reorder the terms: 54 + -3263 + 15x + x2 = 3263 + -3263 Combine like terms: 54 + -3263 = -3209 -3209 + 15x + x2 = 3263 + -3263 Combine like terms: 3263 + -3263 = 0 -3209 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3209' to each side of the equation. -3209 + 15x + 3209 + x2 = 0 + 3209 Reorder the terms: -3209 + 3209 + 15x + x2 = 0 + 3209 Combine like terms: -3209 + 3209 = 0 0 + 15x + x2 = 0 + 3209 15x + x2 = 0 + 3209 Combine like terms: 0 + 3209 = 3209 15x + x2 = 3209 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 3209 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 3209 + 56.25 Combine like terms: 3209 + 56.25 = 3265.25 56.25 + 15x + x2 = 3265.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 3265.25 Calculate the square root of the right side: 57.142366069 Break this problem into two subproblems by setting (x + 7.5) equal to 57.142366069 and -57.142366069.Subproblem 1
x + 7.5 = 57.142366069 Simplifying x + 7.5 = 57.142366069 Reorder the terms: 7.5 + x = 57.142366069 Solving 7.5 + x = 57.142366069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 57.142366069 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 57.142366069 + -7.5 x = 57.142366069 + -7.5 Combine like terms: 57.142366069 + -7.5 = 49.642366069 x = 49.642366069 Simplifying x = 49.642366069Subproblem 2
x + 7.5 = -57.142366069 Simplifying x + 7.5 = -57.142366069 Reorder the terms: 7.5 + x = -57.142366069 Solving 7.5 + x = -57.142366069 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -57.142366069 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -57.142366069 + -7.5 x = -57.142366069 + -7.5 Combine like terms: -57.142366069 + -7.5 = -64.642366069 x = -64.642366069 Simplifying x = -64.642366069Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.642366069, -64.642366069}
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