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Simplifying (7 + x)(2 + x) = 56 Multiply (7 + x) * (2 + x) (7(2 + x) + x(2 + x)) = 56 ((2 * 7 + x * 7) + x(2 + x)) = 56 ((14 + 7x) + x(2 + x)) = 56 (14 + 7x + (2 * x + x * x)) = 56 (14 + 7x + (2x + x2)) = 56 Combine like terms: 7x + 2x = 9x (14 + 9x + x2) = 56 Solving 14 + 9x + x2 = 56 Solving for variable 'x'. Reorder the terms: 14 + -56 + 9x + x2 = 56 + -56 Combine like terms: 14 + -56 = -42 -42 + 9x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -42 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 9x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 9x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 9x + x2 = 0 + 42 9x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 9x + x2 = 42 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 42 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 42 + 20.25 Combine like terms: 42 + 20.25 = 62.25 20.25 + 9x + x2 = 62.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x + 4.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x + 4.5 = 7.889866919 Simplifying x + 4.5 = 7.889866919 Reorder the terms: 4.5 + x = 7.889866919 Solving 4.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 7.889866919 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.889866919 + -4.5 x = 7.889866919 + -4.5 Combine like terms: 7.889866919 + -4.5 = 3.389866919 x = 3.389866919 Simplifying x = 3.389866919Subproblem 2
x + 4.5 = -7.889866919 Simplifying x + 4.5 = -7.889866919 Reorder the terms: 4.5 + x = -7.889866919 Solving 4.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -7.889866919 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.889866919 + -4.5 x = -7.889866919 + -4.5 Combine like terms: -7.889866919 + -4.5 = -12.389866919 x = -12.389866919 Simplifying x = -12.389866919Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.389866919, -12.389866919}
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