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Simplifying 2X2 + -34X + 105 = 0 Reorder the terms: 105 + -34X + 2X2 = 0 Solving 105 + -34X + 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'. 52.5 + -17X + X2 = 0 Move the constant term to the right: Add '-52.5' to each side of the equation. 52.5 + -17X + -52.5 + X2 = 0 + -52.5 Reorder the terms: 52.5 + -52.5 + -17X + X2 = 0 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + -17X + X2 = 0 + -52.5 -17X + X2 = 0 + -52.5 Combine like terms: 0 + -52.5 = -52.5 -17X + X2 = -52.5 The X term is -17X. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17X + 72.25 + X2 = -52.5 + 72.25 Reorder the terms: 72.25 + -17X + X2 = -52.5 + 72.25 Combine like terms: -52.5 + 72.25 = 19.75 72.25 + -17X + X2 = 19.75 Factor a perfect square on the left side: (X + -8.5)(X + -8.5) = 19.75 Calculate the square root of the right side: 4.444097209 Break this problem into two subproblems by setting (X + -8.5) equal to 4.444097209 and -4.444097209.Subproblem 1
X + -8.5 = 4.444097209 Simplifying X + -8.5 = 4.444097209 Reorder the terms: -8.5 + X = 4.444097209 Solving -8.5 + X = 4.444097209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + X = 4.444097209 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + X = 4.444097209 + 8.5 X = 4.444097209 + 8.5 Combine like terms: 4.444097209 + 8.5 = 12.944097209 X = 12.944097209 Simplifying X = 12.944097209Subproblem 2
X + -8.5 = -4.444097209 Simplifying X + -8.5 = -4.444097209 Reorder the terms: -8.5 + X = -4.444097209 Solving -8.5 + X = -4.444097209 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + X = -4.444097209 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + X = -4.444097209 + 8.5 X = -4.444097209 + 8.5 Combine like terms: -4.444097209 + 8.5 = 4.055902791 X = 4.055902791 Simplifying X = 4.055902791Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.944097209, 4.055902791}
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