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Simplifying 4x2 + -17x + 8 = 0 Reorder the terms: 8 + -17x + 4x2 = 0 Solving 8 + -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'. 2 + -4.25x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4.25x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4.25x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4.25x + x2 = 0 + -2 -4.25x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4.25x + x2 = -2 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 = -2 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -2 + 4.515625 Combine like terms: -2 + 4.515625 = 2.515625 4.515625 + -4.25x + x2 = 2.515625 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + -2.125) equal to 1.586072193 and -1.586072193.Subproblem 1
x + -2.125 = 1.586072193 Simplifying x + -2.125 = 1.586072193 Reorder the terms: -2.125 + x = 1.586072193 Solving -2.125 + x = 1.586072193 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 = 1.586072193 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.586072193 + 2.125 x = 1.586072193 + 2.125 Combine like terms: 1.586072193 + 2.125 = 3.711072193 x = 3.711072193 Simplifying x = 3.711072193Subproblem 2
x + -2.125 = -1.586072193 Simplifying x + -2.125 = -1.586072193 Reorder the terms: -2.125 + x = -1.586072193 Solving -2.125 + x = -1.586072193 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 = -1.586072193 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.586072193 + 2.125 x = -1.586072193 + 2.125 Combine like terms: -1.586072193 + 2.125 = 0.538927807 x = 0.538927807 Simplifying x = 0.538927807Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.711072193, 0.538927807}
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