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Simplifying (x + 9)(x + 3) = 54 Reorder the terms: (9 + x)(x + 3) = 54 Reorder the terms: (9 + x)(3 + x) = 54 Multiply (9 + x) * (3 + x) (9(3 + x) + x(3 + x)) = 54 ((3 * 9 + x * 9) + x(3 + x)) = 54 ((27 + 9x) + x(3 + x)) = 54 (27 + 9x + (3 * x + x * x)) = 54 (27 + 9x + (3x + x2)) = 54 Combine like terms: 9x + 3x = 12x (27 + 12x + x2) = 54 Solving 27 + 12x + x2 = 54 Solving for variable 'x'. Reorder the terms: 27 + -54 + 12x + x2 = 54 + -54 Combine like terms: 27 + -54 = -27 -27 + 12x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -27 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 12x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 12x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 12x + x2 = 0 + 27 12x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 12x + x2 = 27 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 27 + 36 Reorder the terms: 36 + 12x + x2 = 27 + 36 Combine like terms: 27 + 36 = 63 36 + 12x + x2 = 63 Factor a perfect square on the left side: (x + 6)(x + 6) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 6) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 6 = 7.937253933 Simplifying x + 6 = 7.937253933 Reorder the terms: 6 + x = 7.937253933 Solving 6 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.937253933 + -6 x = 7.937253933 + -6 Combine like terms: 7.937253933 + -6 = 1.937253933 x = 1.937253933 Simplifying x = 1.937253933Subproblem 2
x + 6 = -7.937253933 Simplifying x + 6 = -7.937253933 Reorder the terms: 6 + x = -7.937253933 Solving 6 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.937253933 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.937253933 + -6 x = -7.937253933 + -6 Combine like terms: -7.937253933 + -6 = -13.937253933 x = -13.937253933 Simplifying x = -13.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.937253933, -13.937253933}
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