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Simplifying 4x2 + -17x + -108 = 0 Reorder the terms: -108 + -17x + 4x2 = 0 Solving -108 + -17x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -27 + -4.25x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -4.25x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -4.25x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -4.25x + x2 = 0 + 27 -4.25x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -4.25x + x2 = 27 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = 27 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = 27 + 4.515625 Combine like terms: 27 + 4.515625 = 31.515625 4.515625 + -4.25x + x2 = 31.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 31.515625 Calculate the square root of the right side: 5.613877893 Break this problem into two subproblems by setting (x + -2.125) equal to 5.613877893 and -5.613877893.Subproblem 1
x + -2.125 = 5.613877893 Simplifying x + -2.125 = 5.613877893 Reorder the terms: -2.125 + x = 5.613877893 Solving -2.125 + x = 5.613877893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 5.613877893 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 5.613877893 + 2.125 x = 5.613877893 + 2.125 Combine like terms: 5.613877893 + 2.125 = 7.738877893 x = 7.738877893 Simplifying x = 7.738877893Subproblem 2
x + -2.125 = -5.613877893 Simplifying x + -2.125 = -5.613877893 Reorder the terms: -2.125 + x = -5.613877893 Solving -2.125 + x = -5.613877893 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -5.613877893 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -5.613877893 + 2.125 x = -5.613877893 + 2.125 Combine like terms: -5.613877893 + 2.125 = -3.488877893 x = -3.488877893 Simplifying x = -3.488877893Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.738877893, -3.488877893}
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