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Simplifying x2 + -3 + 9x + -27 = 0 Reorder the terms: -3 + -27 + 9x + x2 = 0 Combine like terms: -3 + -27 = -30 -30 + 9x + x2 = 0 Solving -30 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 9x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 9x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 9x + x2 = 0 + 30 9x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 9x + x2 = 30 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 = 30 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 30 + 20.25 Combine like terms: 30 + 20.25 = 50.25 20.25 + 9x + x2 = 50.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (x + 4.5) equal to 7.088723439 and -7.088723439.Subproblem 1
x + 4.5 = 7.088723439 Simplifying x + 4.5 = 7.088723439 Reorder the terms: 4.5 + x = 7.088723439 Solving 4.5 + x = 7.088723439 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 = 7.088723439 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 7.088723439 + -4.5 x = 7.088723439 + -4.5 Combine like terms: 7.088723439 + -4.5 = 2.588723439 x = 2.588723439 Simplifying x = 2.588723439Subproblem 2
x + 4.5 = -7.088723439 Simplifying x + 4.5 = -7.088723439 Reorder the terms: 4.5 + x = -7.088723439 Solving 4.5 + x = -7.088723439 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 = -7.088723439 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -7.088723439 + -4.5 x = -7.088723439 + -4.5 Combine like terms: -7.088723439 + -4.5 = -11.588723439 x = -11.588723439 Simplifying x = -11.588723439Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.588723439, -11.588723439}
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