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Simplifying (x + -3)(x + 9) = 27 Reorder the terms: (-3 + x)(x + 9) = 27 Reorder the terms: (-3 + x)(9 + x) = 27 Multiply (-3 + x) * (9 + x) (-3(9 + x) + x(9 + x)) = 27 ((9 * -3 + x * -3) + x(9 + x)) = 27 ((-27 + -3x) + x(9 + x)) = 27 (-27 + -3x + (9 * x + x * x)) = 27 (-27 + -3x + (9x + x2)) = 27 Combine like terms: -3x + 9x = 6x (-27 + 6x + x2) = 27 Solving -27 + 6x + x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + -27 + 6x + x2 = 27 + -27 Combine like terms: -27 + -27 = -54 -54 + 6x + x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -54 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + 6x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + 6x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 6x + x2 = 0 + 54 6x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 6x + x2 = 54 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 = 54 + 9 Reorder the terms: 9 + 6x + x2 = 54 + 9 Combine like terms: 54 + 9 = 63 9 + 6x + x2 = 63 Factor a perfect square on the left side: (x + 3)(x + 3) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 3) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 3 = 7.937253933 Simplifying x + 3 = 7.937253933 Reorder the terms: 3 + x = 7.937253933 Solving 3 + x = 7.937253933 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 = 7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.937253933 + -3 x = 7.937253933 + -3 Combine like terms: 7.937253933 + -3 = 4.937253933 x = 4.937253933 Simplifying x = 4.937253933Subproblem 2
x + 3 = -7.937253933 Simplifying x + 3 = -7.937253933 Reorder the terms: 3 + x = -7.937253933 Solving 3 + x = -7.937253933 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 = -7.937253933 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.937253933 + -3 x = -7.937253933 + -3 Combine like terms: -7.937253933 + -3 = -10.937253933 x = -10.937253933 Simplifying x = -10.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.937253933, -10.937253933}
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