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Simplifying (11 + x)(7 + x) = 154 Multiply (11 + x) * (7 + x) (11(7 + x) + x(7 + x)) = 154 ((7 * 11 + x * 11) + x(7 + x)) = 154 ((77 + 11x) + x(7 + x)) = 154 (77 + 11x + (7 * x + x * x)) = 154 (77 + 11x + (7x + x2)) = 154 Combine like terms: 11x + 7x = 18x (77 + 18x + x2) = 154 Solving 77 + 18x + x2 = 154 Solving for variable 'x'. Reorder the terms: 77 + -154 + 18x + x2 = 154 + -154 Combine like terms: 77 + -154 = -77 -77 + 18x + x2 = 154 + -154 Combine like terms: 154 + -154 = 0 -77 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + 18x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + 18x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + 18x + x2 = 0 + 77 18x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 18x + x2 = 77 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 77 + 81 Reorder the terms: 81 + 18x + x2 = 77 + 81 Combine like terms: 77 + 81 = 158 81 + 18x + x2 = 158 Factor a perfect square on the left side: (x + 9)(x + 9) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (x + 9) equal to 12.56980509 and -12.56980509.Subproblem 1
x + 9 = 12.56980509 Simplifying x + 9 = 12.56980509 Reorder the terms: 9 + x = 12.56980509 Solving 9 + x = 12.56980509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 12.56980509 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.56980509 + -9 x = 12.56980509 + -9 Combine like terms: 12.56980509 + -9 = 3.56980509 x = 3.56980509 Simplifying x = 3.56980509Subproblem 2
x + 9 = -12.56980509 Simplifying x + 9 = -12.56980509 Reorder the terms: 9 + x = -12.56980509 Solving 9 + x = -12.56980509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -12.56980509 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.56980509 + -9 x = -12.56980509 + -9 Combine like terms: -12.56980509 + -9 = -21.56980509 x = -21.56980509 Simplifying x = -21.56980509Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.56980509, -21.56980509}
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