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Simplifying 34 = 105x + -16x2 Solving 34 = 105x + -16x2 Solving for variable 'x'. Reorder the terms: 34 + -105x + 16x2 = 105x + -105x + -16x2 + 16x2 Combine like terms: 105x + -105x = 0 34 + -105x + 16x2 = 0 + -16x2 + 16x2 34 + -105x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 34 + -105x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 2.125 + -6.5625x + x2 = 0 Move the constant term to the right: Add '-2.125' to each side of the equation. 2.125 + -6.5625x + -2.125 + x2 = 0 + -2.125 Reorder the terms: 2.125 + -2.125 + -6.5625x + x2 = 0 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + -6.5625x + x2 = 0 + -2.125 -6.5625x + x2 = 0 + -2.125 Combine like terms: 0 + -2.125 = -2.125 -6.5625x + x2 = -2.125 The x term is -6.5625x. Take half its coefficient (-3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. -6.5625x + 10.76660156 + x2 = -2.125 + 10.76660156 Reorder the terms: 10.76660156 + -6.5625x + x2 = -2.125 + 10.76660156 Combine like terms: -2.125 + 10.76660156 = 8.64160156 10.76660156 + -6.5625x + x2 = 8.64160156 Factor a perfect square on the left side: (x + -3.28125)(x + -3.28125) = 8.64160156 Calculate the square root of the right side: 2.93966011 Break this problem into two subproblems by setting (x + -3.28125) equal to 2.93966011 and -2.93966011.Subproblem 1
x + -3.28125 = 2.93966011 Simplifying x + -3.28125 = 2.93966011 Reorder the terms: -3.28125 + x = 2.93966011 Solving -3.28125 + x = 2.93966011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + x = 2.93966011 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + x = 2.93966011 + 3.28125 x = 2.93966011 + 3.28125 Combine like terms: 2.93966011 + 3.28125 = 6.22091011 x = 6.22091011 Simplifying x = 6.22091011Subproblem 2
x + -3.28125 = -2.93966011 Simplifying x + -3.28125 = -2.93966011 Reorder the terms: -3.28125 + x = -2.93966011 Solving -3.28125 + x = -2.93966011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.28125' to each side of the equation. -3.28125 + 3.28125 + x = -2.93966011 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + x = -2.93966011 + 3.28125 x = -2.93966011 + 3.28125 Combine like terms: -2.93966011 + 3.28125 = 0.34158989 x = 0.34158989 Simplifying x = 0.34158989Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.22091011, 0.34158989}
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