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Simplifying 16x2 + -9x + -49 = 0 Reorder the terms: -49 + -9x + 16x2 = 0 Solving -49 + -9x + 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'. -3.0625 + -0.5625x + x2 = 0 Move the constant term to the right: Add '3.0625' to each side of the equation. -3.0625 + -0.5625x + 3.0625 + x2 = 0 + 3.0625 Reorder the terms: -3.0625 + 3.0625 + -0.5625x + x2 = 0 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + -0.5625x + x2 = 0 + 3.0625 -0.5625x + x2 = 0 + 3.0625 Combine like terms: 0 + 3.0625 = 3.0625 -0.5625x + x2 = 3.0625 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = 3.0625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = 3.0625 + 0.0791015625 Combine like terms: 3.0625 + 0.0791015625 = 3.1416015625 0.0791015625 + -0.5625x + x2 = 3.1416015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 3.1416015625 Calculate the square root of the right side: 1.772456364 Break this problem into two subproblems by setting (x + -0.28125) equal to 1.772456364 and -1.772456364.Subproblem 1
x + -0.28125 = 1.772456364 Simplifying x + -0.28125 = 1.772456364 Reorder the terms: -0.28125 + x = 1.772456364 Solving -0.28125 + x = 1.772456364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 1.772456364 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 1.772456364 + 0.28125 x = 1.772456364 + 0.28125 Combine like terms: 1.772456364 + 0.28125 = 2.053706364 x = 2.053706364 Simplifying x = 2.053706364Subproblem 2
x + -0.28125 = -1.772456364 Simplifying x + -0.28125 = -1.772456364 Reorder the terms: -0.28125 + x = -1.772456364 Solving -0.28125 + x = -1.772456364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -1.772456364 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -1.772456364 + 0.28125 x = -1.772456364 + 0.28125 Combine like terms: -1.772456364 + 0.28125 = -1.491206364 x = -1.491206364 Simplifying x = -1.491206364Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.053706364, -1.491206364}
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