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Simplifying (x + -3)(x + -3) = 27 Reorder the terms: (-3 + x)(x + -3) = 27 Reorder the terms: (-3 + x)(-3 + x) = 27 Multiply (-3 + x) * (-3 + x) (-3(-3 + x) + x(-3 + x)) = 27 ((-3 * -3 + x * -3) + x(-3 + x)) = 27 ((9 + -3x) + x(-3 + x)) = 27 (9 + -3x + (-3 * x + x * x)) = 27 (9 + -3x + (-3x + x2)) = 27 Combine like terms: -3x + -3x = -6x (9 + -6x + x2) = 27 Solving 9 + -6x + x2 = 27 Solving for variable 'x'. Reorder the terms: 9 + -27 + -6x + x2 = 27 + -27 Combine like terms: 9 + -27 = -18 -18 + -6x + x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -18 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -6x + x2 = 0 + 18 -6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -6x + x2 = 18 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 = 18 + 9 Reorder the terms: 9 + -6x + x2 = 18 + 9 Combine like terms: 18 + 9 = 27 9 + -6x + x2 = 27 Factor a perfect square on the left side: (x + -3)(x + -3) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (x + -3) equal to 5.196152423 and -5.196152423.Subproblem 1
x + -3 = 5.196152423 Simplifying x + -3 = 5.196152423 Reorder the terms: -3 + x = 5.196152423 Solving -3 + x = 5.196152423 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 = 5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.196152423 + 3 x = 5.196152423 + 3 Combine like terms: 5.196152423 + 3 = 8.196152423 x = 8.196152423 Simplifying x = 8.196152423Subproblem 2
x + -3 = -5.196152423 Simplifying x + -3 = -5.196152423 Reorder the terms: -3 + x = -5.196152423 Solving -3 + x = -5.196152423 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 = -5.196152423 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.196152423 + 3 x = -5.196152423 + 3 Combine like terms: -5.196152423 + 3 = -2.196152423 x = -2.196152423 Simplifying x = -2.196152423Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.196152423, -2.196152423}
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