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Simplifying 2X2 + -5X + -48 = 0 Reorder the terms: -48 + -5X + 2X2 = 0 Solving -48 + -5X + 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 + -2.5X + X2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + -2.5X + 24 + X2 = 0 + 24 Reorder the terms: -24 + 24 + -2.5X + X2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -2.5X + X2 = 0 + 24 -2.5X + X2 = 0 + 24 Combine like terms: 0 + 24 = 24 -2.5X + X2 = 24 The X term is -2.5X. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5X + 1.5625 + X2 = 24 + 1.5625 Reorder the terms: 1.5625 + -2.5X + X2 = 24 + 1.5625 Combine like terms: 24 + 1.5625 = 25.5625 1.5625 + -2.5X + X2 = 25.5625 Factor a perfect square on the left side: (X + -1.25)(X + -1.25) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (X + -1.25) equal to 5.055937104 and -5.055937104.Subproblem 1
X + -1.25 = 5.055937104 Simplifying X + -1.25 = 5.055937104 Reorder the terms: -1.25 + X = 5.055937104 Solving -1.25 + X = 5.055937104 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = 5.055937104 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = 5.055937104 + 1.25 X = 5.055937104 + 1.25 Combine like terms: 5.055937104 + 1.25 = 6.305937104 X = 6.305937104 Simplifying X = 6.305937104Subproblem 2
X + -1.25 = -5.055937104 Simplifying X + -1.25 = -5.055937104 Reorder the terms: -1.25 + X = -5.055937104 Solving -1.25 + X = -5.055937104 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + X = -5.055937104 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + X = -5.055937104 + 1.25 X = -5.055937104 + 1.25 Combine like terms: -5.055937104 + 1.25 = -3.805937104 X = -3.805937104 Simplifying X = -3.805937104Solution
The solution to the problem is based on the solutions from the subproblems. X = {6.305937104, -3.805937104}
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