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Simplifying 16x2 + 12x + -25 = 0 Reorder the terms: -25 + 12x + 16x2 = 0 Solving -25 + 12x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.75x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.75x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.75x + x2 = 0 + 1.5625 0.75x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.75x + x2 = 1.5625 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1.5625 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1.5625 + 0.140625 Combine like terms: 1.5625 + 0.140625 = 1.703125 0.140625 + 0.75x + x2 = 1.703125 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.703125 Calculate the square root of the right side: 1.305038314 Break this problem into two subproblems by setting (x + 0.375) equal to 1.305038314 and -1.305038314.Subproblem 1
x + 0.375 = 1.305038314 Simplifying x + 0.375 = 1.305038314 Reorder the terms: 0.375 + x = 1.305038314 Solving 0.375 + x = 1.305038314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.305038314 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.305038314 + -0.375 x = 1.305038314 + -0.375 Combine like terms: 1.305038314 + -0.375 = 0.930038314 x = 0.930038314 Simplifying x = 0.930038314Subproblem 2
x + 0.375 = -1.305038314 Simplifying x + 0.375 = -1.305038314 Reorder the terms: 0.375 + x = -1.305038314 Solving 0.375 + x = -1.305038314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.305038314 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.305038314 + -0.375 x = -1.305038314 + -0.375 Combine like terms: -1.305038314 + -0.375 = -1.680038314 x = -1.680038314 Simplifying x = -1.680038314Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.930038314, -1.680038314}
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