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Simplifying -16x2 + -105x + -34 = 0 Reorder the terms: -34 + -105x + -16x2 = 0 Solving -34 + -105x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(34 + 105x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(34 + 105x + 16x2)' equal to zero and attempt to solve: Simplifying 34 + 105x + 16x2 = 0 Solving 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 = -0.34158989 x = -0.34158989 Simplifying x = -0.34158989Subproblem 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 = -6.22091011 x = -6.22091011 Simplifying x = -6.22091011Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.34158989, -6.22091011}Solution
x = {-0.34158989, -6.22091011}
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