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Simplifying 16x2 + 44x + 25 = 0 Reorder the terms: 25 + 44x + 16x2 = 0 Solving 25 + 44x + 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'. 1.5625 + 2.75x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + 2.75x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + 2.75x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + 2.75x + x2 = 0 + -1.5625 2.75x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 2.75x + x2 = -1.5625 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = -1.5625 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = -1.5625 + 1.890625 Combine like terms: -1.5625 + 1.890625 = 0.328125 1.890625 + 2.75x + x2 = 0.328125 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 0.328125 Calculate the square root of the right side: 0.572821962 Break this problem into two subproblems by setting (x + 1.375) equal to 0.572821962 and -0.572821962.Subproblem 1
x + 1.375 = 0.572821962 Simplifying x + 1.375 = 0.572821962 Reorder the terms: 1.375 + x = 0.572821962 Solving 1.375 + x = 0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 0.572821962 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 0.572821962 + -1.375 x = 0.572821962 + -1.375 Combine like terms: 0.572821962 + -1.375 = -0.802178038 x = -0.802178038 Simplifying x = -0.802178038Subproblem 2
x + 1.375 = -0.572821962 Simplifying x + 1.375 = -0.572821962 Reorder the terms: 1.375 + x = -0.572821962 Solving 1.375 + x = -0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -0.572821962 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -0.572821962 + -1.375 x = -0.572821962 + -1.375 Combine like terms: -0.572821962 + -1.375 = -1.947821962 x = -1.947821962 Simplifying x = -1.947821962Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.802178038, -1.947821962}
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