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Simplifying 2x2 + -7x + -48 = 0 Reorder the terms: -48 + -7x + 2x2 = 0 Solving -48 + -7x + 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'. -24 + -3.5x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -3.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -3.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -3.5x + x2 = 0 + 24 -3.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -3.5x + x2 = 24 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 24 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 24 + 3.0625 Combine like terms: 24 + 3.0625 = 27.0625 3.0625 + -3.5x + x2 = 27.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 27.0625 Calculate the square root of the right side: 5.202163012 Break this problem into two subproblems by setting (x + -1.75) equal to 5.202163012 and -5.202163012.Subproblem 1
x + -1.75 = 5.202163012 Simplifying x + -1.75 = 5.202163012 Reorder the terms: -1.75 + x = 5.202163012 Solving -1.75 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 5.202163012 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 5.202163012 + 1.75 x = 5.202163012 + 1.75 Combine like terms: 5.202163012 + 1.75 = 6.952163012 x = 6.952163012 Simplifying x = 6.952163012Subproblem 2
x + -1.75 = -5.202163012 Simplifying x + -1.75 = -5.202163012 Reorder the terms: -1.75 + x = -5.202163012 Solving -1.75 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -5.202163012 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -5.202163012 + 1.75 x = -5.202163012 + 1.75 Combine like terms: -5.202163012 + 1.75 = -3.452163012 x = -3.452163012 Simplifying x = -3.452163012Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.952163012, -3.452163012}
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