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Simplifying (x + 6)(x + 9) = 13 Reorder the terms: (6 + x)(x + 9) = 13 Reorder the terms: (6 + x)(9 + x) = 13 Multiply (6 + x) * (9 + x) (6(9 + x) + x(9 + x)) = 13 ((9 * 6 + x * 6) + x(9 + x)) = 13 ((54 + 6x) + x(9 + x)) = 13 (54 + 6x + (9 * x + x * x)) = 13 (54 + 6x + (9x + x2)) = 13 Combine like terms: 6x + 9x = 15x (54 + 15x + x2) = 13 Solving 54 + 15x + x2 = 13 Solving for variable 'x'. Reorder the terms: 54 + -13 + 15x + x2 = 13 + -13 Combine like terms: 54 + -13 = 41 41 + 15x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 41 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + 15x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + 15x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + 15x + x2 = 0 + -41 15x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 15x + x2 = -41 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = -41 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -41 + 56.25 Combine like terms: -41 + 56.25 = 15.25 56.25 + 15x + x2 = 15.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + 7.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + 7.5 = 3.905124838 Simplifying x + 7.5 = 3.905124838 Reorder the terms: 7.5 + x = 3.905124838 Solving 7.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 3.905124838 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 3.905124838 + -7.5 x = 3.905124838 + -7.5 Combine like terms: 3.905124838 + -7.5 = -3.594875162 x = -3.594875162 Simplifying x = -3.594875162Subproblem 2
x + 7.5 = -3.905124838 Simplifying x + 7.5 = -3.905124838 Reorder the terms: 7.5 + x = -3.905124838 Solving 7.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -3.905124838 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -3.905124838 + -7.5 x = -3.905124838 + -7.5 Combine like terms: -3.905124838 + -7.5 = -11.405124838 x = -11.405124838 Simplifying x = -11.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.594875162, -11.405124838}
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