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Simplifying x2 + 6x + -108 = -9 Reorder the terms: -108 + 6x + x2 = -9 Solving -108 + 6x + x2 = -9 Solving for variable 'x'. Reorder the terms: -108 + 9 + 6x + x2 = -9 + 9 Combine like terms: -108 + 9 = -99 -99 + 6x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -99 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 6x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 6x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 6x + x2 = 0 + 99 6x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 6x + x2 = 99 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 = 99 + 9 Reorder the terms: 9 + 6x + x2 = 99 + 9 Combine like terms: 99 + 9 = 108 9 + 6x + x2 = 108 Factor a perfect square on the left side: (x + 3)(x + 3) = 108 Calculate the square root of the right side: 10.392304845 Break this problem into two subproblems by setting (x + 3) equal to 10.392304845 and -10.392304845.Subproblem 1
x + 3 = 10.392304845 Simplifying x + 3 = 10.392304845 Reorder the terms: 3 + x = 10.392304845 Solving 3 + x = 10.392304845 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 = 10.392304845 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.392304845 + -3 x = 10.392304845 + -3 Combine like terms: 10.392304845 + -3 = 7.392304845 x = 7.392304845 Simplifying x = 7.392304845Subproblem 2
x + 3 = -10.392304845 Simplifying x + 3 = -10.392304845 Reorder the terms: 3 + x = -10.392304845 Solving 3 + x = -10.392304845 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 = -10.392304845 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.392304845 + -3 x = -10.392304845 + -3 Combine like terms: -10.392304845 + -3 = -13.392304845 x = -13.392304845 Simplifying x = -13.392304845Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.392304845, -13.392304845}
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