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Simplifying 2x2 + -9x + -44 = 0 Reorder the terms: -44 + -9x + 2x2 = 0 Solving -44 + -9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22 + -4.5x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -4.5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -4.5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -4.5x + x2 = 0 + 22 -4.5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -4.5x + x2 = 22 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = 22 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 22 + 5.0625 Combine like terms: 22 + 5.0625 = 27.0625 5.0625 + -4.5x + x2 = 27.0625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (x + -2.25) equal to 5.202163012 and -5.202163012.Subproblem 1
x + -2.25 = 5.202163012 Simplifying x + -2.25 = 5.202163012 Reorder the terms: -2.25 + x = 5.202163012 Solving -2.25 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 5.202163012 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 5.202163012 + 2.25 x = 5.202163012 + 2.25 Combine like terms: 5.202163012 + 2.25 = 7.452163012 x = 7.452163012 Simplifying x = 7.452163012Subproblem 2
x + -2.25 = -5.202163012 Simplifying x + -2.25 = -5.202163012 Reorder the terms: -2.25 + x = -5.202163012 Solving -2.25 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -5.202163012 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -5.202163012 + 2.25 x = -5.202163012 + 2.25 Combine like terms: -5.202163012 + 2.25 = -2.952163012 x = -2.952163012 Simplifying x = -2.952163012Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.452163012, -2.952163012}
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