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Simplifying (x + 2)(x + 5) = 72 Reorder the terms: (2 + x)(x + 5) = 72 Reorder the terms: (2 + x)(5 + x) = 72 Multiply (2 + x) * (5 + x) (2(5 + x) + x(5 + x)) = 72 ((5 * 2 + x * 2) + x(5 + x)) = 72 ((10 + 2x) + x(5 + x)) = 72 (10 + 2x + (5 * x + x * x)) = 72 (10 + 2x + (5x + x2)) = 72 Combine like terms: 2x + 5x = 7x (10 + 7x + x2) = 72 Solving 10 + 7x + x2 = 72 Solving for variable 'x'. Reorder the terms: 10 + -72 + 7x + x2 = 72 + -72 Combine like terms: 10 + -72 = -62 -62 + 7x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 -62 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 7x + 62 + x2 = 0 + 62 Reorder the terms: -62 + 62 + 7x + x2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 7x + x2 = 0 + 62 7x + x2 = 0 + 62 Combine like terms: 0 + 62 = 62 7x + x2 = 62 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 = 62 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 62 + 12.25 Combine like terms: 62 + 12.25 = 74.25 12.25 + 7x + x2 = 74.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (x + 3.5) equal to 8.61684397 and -8.61684397.Subproblem 1
x + 3.5 = 8.61684397 Simplifying x + 3.5 = 8.61684397 Reorder the terms: 3.5 + x = 8.61684397 Solving 3.5 + x = 8.61684397 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 = 8.61684397 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 8.61684397 + -3.5 x = 8.61684397 + -3.5 Combine like terms: 8.61684397 + -3.5 = 5.11684397 x = 5.11684397 Simplifying x = 5.11684397Subproblem 2
x + 3.5 = -8.61684397 Simplifying x + 3.5 = -8.61684397 Reorder the terms: 3.5 + x = -8.61684397 Solving 3.5 + x = -8.61684397 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 = -8.61684397 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -8.61684397 + -3.5 x = -8.61684397 + -3.5 Combine like terms: -8.61684397 + -3.5 = -12.11684397 x = -12.11684397 Simplifying x = -12.11684397Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.11684397, -12.11684397}
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