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Simplifying (1 + x)(x + 5) = 280 Reorder the terms: (1 + x)(5 + x) = 280 Multiply (1 + x) * (5 + x) (1(5 + x) + x(5 + x)) = 280 ((5 * 1 + x * 1) + x(5 + x)) = 280 ((5 + 1x) + x(5 + x)) = 280 (5 + 1x + (5 * x + x * x)) = 280 (5 + 1x + (5x + x2)) = 280 Combine like terms: 1x + 5x = 6x (5 + 6x + x2) = 280 Solving 5 + 6x + x2 = 280 Solving for variable 'x'. Reorder the terms: 5 + -280 + 6x + x2 = 280 + -280 Combine like terms: 5 + -280 = -275 -275 + 6x + x2 = 280 + -280 Combine like terms: 280 + -280 = 0 -275 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '275' to each side of the equation. -275 + 6x + 275 + x2 = 0 + 275 Reorder the terms: -275 + 275 + 6x + x2 = 0 + 275 Combine like terms: -275 + 275 = 0 0 + 6x + x2 = 0 + 275 6x + x2 = 0 + 275 Combine like terms: 0 + 275 = 275 6x + x2 = 275 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 275 + 9 Reorder the terms: 9 + 6x + x2 = 275 + 9 Combine like terms: 275 + 9 = 284 9 + 6x + x2 = 284 Factor a perfect square on the left side: (x + 3)(x + 3) = 284 Calculate the square root of the right side: 16.852299546 Break this problem into two subproblems by setting (x + 3) equal to 16.852299546 and -16.852299546.Subproblem 1
x + 3 = 16.852299546 Simplifying x + 3 = 16.852299546 Reorder the terms: 3 + x = 16.852299546 Solving 3 + x = 16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 16.852299546 + -3 Combine like terms: 3 + -3 = 0 0 + x = 16.852299546 + -3 x = 16.852299546 + -3 Combine like terms: 16.852299546 + -3 = 13.852299546 x = 13.852299546 Simplifying x = 13.852299546Subproblem 2
x + 3 = -16.852299546 Simplifying x + 3 = -16.852299546 Reorder the terms: 3 + x = -16.852299546 Solving 3 + x = -16.852299546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -16.852299546 + -3 Combine like terms: 3 + -3 = 0 0 + x = -16.852299546 + -3 x = -16.852299546 + -3 Combine like terms: -16.852299546 + -3 = -19.852299546 x = -19.852299546 Simplifying x = -19.852299546Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.852299546, -19.852299546}
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