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Simplifying 2x2 + -19x + -9 = 0 Reorder the terms: -9 + -19x + 2x2 = 0 Solving -9 + -19x + 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'. -4.5 + -9.5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -9.5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -9.5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -9.5x + x2 = 0 + 4.5 -9.5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -9.5x + x2 = 4.5 The x term is -9.5x. Take half its coefficient (-4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. -9.5x + 22.5625 + x2 = 4.5 + 22.5625 Reorder the terms: 22.5625 + -9.5x + x2 = 4.5 + 22.5625 Combine like terms: 4.5 + 22.5625 = 27.0625 22.5625 + -9.5x + x2 = 27.0625 Factor a perfect square on the left side: (x + -4.75)(x + -4.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (x + -4.75) equal to 5.202163012 and -5.202163012.Subproblem 1
x + -4.75 = 5.202163012 Simplifying x + -4.75 = 5.202163012 Reorder the terms: -4.75 + x = 5.202163012 Solving -4.75 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 5.202163012 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 5.202163012 + 4.75 x = 5.202163012 + 4.75 Combine like terms: 5.202163012 + 4.75 = 9.952163012 x = 9.952163012 Simplifying x = 9.952163012Subproblem 2
x + -4.75 = -5.202163012 Simplifying x + -4.75 = -5.202163012 Reorder the terms: -4.75 + x = -5.202163012 Solving -4.75 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -5.202163012 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -5.202163012 + 4.75 x = -5.202163012 + 4.75 Combine like terms: -5.202163012 + 4.75 = -0.452163012 x = -0.452163012 Simplifying x = -0.452163012Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.952163012, -0.452163012}
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