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Simplifying 16x2 + -29x + 4 = 0 Reorder the terms: 4 + -29x + 16x2 = 0 Solving 4 + -29x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + -1.8125x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.8125x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.8125x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.8125x + x2 = 0 + -0.25 -1.8125x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.8125x + x2 = -0.25 The x term is -1.8125x. Take half its coefficient (-0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. -1.8125x + 0.8212890625 + x2 = -0.25 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = -0.25 + 0.8212890625 Combine like terms: -0.25 + 0.8212890625 = 0.5712890625 0.8212890625 + -1.8125x + x2 = 0.5712890625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 0.5712890625 Calculate the square root of the right side: 0.755836664 Break this problem into two subproblems by setting (x + -0.90625) equal to 0.755836664 and -0.755836664.Subproblem 1
x + -0.90625 = 0.755836664 Simplifying x + -0.90625 = 0.755836664 Reorder the terms: -0.90625 + x = 0.755836664 Solving -0.90625 + x = 0.755836664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = 0.755836664 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 0.755836664 + 0.90625 x = 0.755836664 + 0.90625 Combine like terms: 0.755836664 + 0.90625 = 1.662086664 x = 1.662086664 Simplifying x = 1.662086664Subproblem 2
x + -0.90625 = -0.755836664 Simplifying x + -0.90625 = -0.755836664 Reorder the terms: -0.90625 + x = -0.755836664 Solving -0.90625 + x = -0.755836664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.90625' to each side of the equation. -0.90625 + 0.90625 + x = -0.755836664 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -0.755836664 + 0.90625 x = -0.755836664 + 0.90625 Combine like terms: -0.755836664 + 0.90625 = 0.150413336 x = 0.150413336 Simplifying x = 0.150413336Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.662086664, 0.150413336}
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