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Simplifying 16x2 + -8x + -47 = 0 Reorder the terms: -47 + -8x + 16x2 = 0 Solving -47 + -8x + 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'. -2.9375 + -0.5x + x2 = 0 Move the constant term to the right: Add '2.9375' to each side of the equation. -2.9375 + -0.5x + 2.9375 + x2 = 0 + 2.9375 Reorder the terms: -2.9375 + 2.9375 + -0.5x + x2 = 0 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + -0.5x + x2 = 0 + 2.9375 -0.5x + x2 = 0 + 2.9375 Combine like terms: 0 + 2.9375 = 2.9375 -0.5x + x2 = 2.9375 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 2.9375 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 2.9375 + 0.0625 Combine like terms: 2.9375 + 0.0625 = 3 0.0625 + -0.5x + x2 = 3 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -0.25) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -0.25 = 1.732050808 Simplifying x + -0.25 = 1.732050808 Reorder the terms: -0.25 + x = 1.732050808 Solving -0.25 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.732050808 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.732050808 + 0.25 x = 1.732050808 + 0.25 Combine like terms: 1.732050808 + 0.25 = 1.982050808 x = 1.982050808 Simplifying x = 1.982050808Subproblem 2
x + -0.25 = -1.732050808 Simplifying x + -0.25 = -1.732050808 Reorder the terms: -0.25 + x = -1.732050808 Solving -0.25 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.732050808 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.732050808 + 0.25 x = -1.732050808 + 0.25 Combine like terms: -1.732050808 + 0.25 = -1.482050808 x = -1.482050808 Simplifying x = -1.482050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.982050808, -1.482050808}
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