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Simplifying (x + 5)(x + 2) = 355 Reorder the terms: (5 + x)(x + 2) = 355 Reorder the terms: (5 + x)(2 + x) = 355 Multiply (5 + x) * (2 + x) (5(2 + x) + x(2 + x)) = 355 ((2 * 5 + x * 5) + x(2 + x)) = 355 ((10 + 5x) + x(2 + x)) = 355 (10 + 5x + (2 * x + x * x)) = 355 (10 + 5x + (2x + x2)) = 355 Combine like terms: 5x + 2x = 7x (10 + 7x + x2) = 355 Solving 10 + 7x + x2 = 355 Solving for variable 'x'. Reorder the terms: 10 + -355 + 7x + x2 = 355 + -355 Combine like terms: 10 + -355 = -345 -345 + 7x + x2 = 355 + -355 Combine like terms: 355 + -355 = 0 -345 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '345' to each side of the equation. -345 + 7x + 345 + x2 = 0 + 345 Reorder the terms: -345 + 345 + 7x + x2 = 0 + 345 Combine like terms: -345 + 345 = 0 0 + 7x + x2 = 0 + 345 7x + x2 = 0 + 345 Combine like terms: 0 + 345 = 345 7x + x2 = 345 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 345 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 345 + 12.25 Combine like terms: 345 + 12.25 = 357.25 12.25 + 7x + x2 = 357.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 357.25 Calculate the square root of the right side: 18.901058171 Break this problem into two subproblems by setting (x + 3.5) equal to 18.901058171 and -18.901058171.Subproblem 1
x + 3.5 = 18.901058171 Simplifying x + 3.5 = 18.901058171 Reorder the terms: 3.5 + x = 18.901058171 Solving 3.5 + x = 18.901058171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 18.901058171 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 18.901058171 + -3.5 x = 18.901058171 + -3.5 Combine like terms: 18.901058171 + -3.5 = 15.401058171 x = 15.401058171 Simplifying x = 15.401058171Subproblem 2
x + 3.5 = -18.901058171 Simplifying x + 3.5 = -18.901058171 Reorder the terms: 3.5 + x = -18.901058171 Solving 3.5 + x = -18.901058171 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -18.901058171 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -18.901058171 + -3.5 x = -18.901058171 + -3.5 Combine like terms: -18.901058171 + -3.5 = -22.401058171 x = -22.401058171 Simplifying x = -22.401058171Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.401058171, -22.401058171}
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