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Simplifying (x + 7)(x + 2) = 180 Reorder the terms: (7 + x)(x + 2) = 180 Reorder the terms: (7 + x)(2 + x) = 180 Multiply (7 + x) * (2 + x) (7(2 + x) + x(2 + x)) = 180 ((2 * 7 + x * 7) + x(2 + x)) = 180 ((14 + 7x) + x(2 + x)) = 180 (14 + 7x + (2 * x + x * x)) = 180 (14 + 7x + (2x + x2)) = 180 Combine like terms: 7x + 2x = 9x (14 + 9x + x2) = 180 Solving 14 + 9x + x2 = 180 Solving for variable 'x'. Reorder the terms: 14 + -180 + 9x + x2 = 180 + -180 Combine like terms: 14 + -180 = -166 -166 + 9x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -166 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '166' to each side of the equation. -166 + 9x + 166 + x2 = 0 + 166 Reorder the terms: -166 + 166 + 9x + x2 = 0 + 166 Combine like terms: -166 + 166 = 0 0 + 9x + x2 = 0 + 166 9x + x2 = 0 + 166 Combine like terms: 0 + 166 = 166 9x + x2 = 166 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 = 166 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 166 + 20.25 Combine like terms: 166 + 20.25 = 186.25 20.25 + 9x + x2 = 186.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 186.25 Calculate the square root of the right side: 13.647344064 Break this problem into two subproblems by setting (x + 4.5) equal to 13.647344064 and -13.647344064.Subproblem 1
x + 4.5 = 13.647344064 Simplifying x + 4.5 = 13.647344064 Reorder the terms: 4.5 + x = 13.647344064 Solving 4.5 + x = 13.647344064 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 = 13.647344064 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 13.647344064 + -4.5 x = 13.647344064 + -4.5 Combine like terms: 13.647344064 + -4.5 = 9.147344064 x = 9.147344064 Simplifying x = 9.147344064Subproblem 2
x + 4.5 = -13.647344064 Simplifying x + 4.5 = -13.647344064 Reorder the terms: 4.5 + x = -13.647344064 Solving 4.5 + x = -13.647344064 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 = -13.647344064 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -13.647344064 + -4.5 x = -13.647344064 + -4.5 Combine like terms: -13.647344064 + -4.5 = -18.147344064 x = -18.147344064 Simplifying x = -18.147344064Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.147344064, -18.147344064}
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