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Simplifying x2 + 9x + -138 = 0 Reorder the terms: -138 + 9x + x2 = 0 Solving -138 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + 9x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + 9x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + 9x + x2 = 0 + 138 9x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 9x + x2 = 138 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 138 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 138 + 20.25 Combine like terms: 138 + 20.25 = 158.25 20.25 + 9x + x2 = 158.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 158.25 Calculate the square root of the right side: 12.579745625 Break this problem into two subproblems by setting (x + 4.5) equal to 12.579745625 and -12.579745625.Subproblem 1
x + 4.5 = 12.579745625 Simplifying x + 4.5 = 12.579745625 Reorder the terms: 4.5 + x = 12.579745625 Solving 4.5 + x = 12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 12.579745625 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 12.579745625 + -4.5 x = 12.579745625 + -4.5 Combine like terms: 12.579745625 + -4.5 = 8.079745625 x = 8.079745625 Simplifying x = 8.079745625Subproblem 2
x + 4.5 = -12.579745625 Simplifying x + 4.5 = -12.579745625 Reorder the terms: 4.5 + x = -12.579745625 Solving 4.5 + x = -12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -12.579745625 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -12.579745625 + -4.5 x = -12.579745625 + -4.5 Combine like terms: -12.579745625 + -4.5 = -17.079745625 x = -17.079745625 Simplifying x = -17.079745625Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.079745625, -17.079745625}
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