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Simplifying 16x2 + 8x = 181 Reorder the terms: 8x + 16x2 = 181 Solving 8x + 16x2 = 181 Solving for variable 'x'. Reorder the terms: -181 + 8x + 16x2 = 181 + -181 Combine like terms: 181 + -181 = 0 -181 + 8x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -11.3125 + 0.5x + x2 = 0 Move the constant term to the right: Add '11.3125' to each side of the equation. -11.3125 + 0.5x + 11.3125 + x2 = 0 + 11.3125 Reorder the terms: -11.3125 + 11.3125 + 0.5x + x2 = 0 + 11.3125 Combine like terms: -11.3125 + 11.3125 = 0.0000 0.0000 + 0.5x + x2 = 0 + 11.3125 0.5x + x2 = 0 + 11.3125 Combine like terms: 0 + 11.3125 = 11.3125 0.5x + x2 = 11.3125 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 = 11.3125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 11.3125 + 0.0625 Combine like terms: 11.3125 + 0.0625 = 11.375 0.0625 + 0.5x + x2 = 11.375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 11.375 Calculate the square root of the right side: 3.372684391 Break this problem into two subproblems by setting (x + 0.25) equal to 3.372684391 and -3.372684391.Subproblem 1
x + 0.25 = 3.372684391 Simplifying x + 0.25 = 3.372684391 Reorder the terms: 0.25 + x = 3.372684391 Solving 0.25 + x = 3.372684391 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 = 3.372684391 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.372684391 + -0.25 x = 3.372684391 + -0.25 Combine like terms: 3.372684391 + -0.25 = 3.122684391 x = 3.122684391 Simplifying x = 3.122684391Subproblem 2
x + 0.25 = -3.372684391 Simplifying x + 0.25 = -3.372684391 Reorder the terms: 0.25 + x = -3.372684391 Solving 0.25 + x = -3.372684391 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 = -3.372684391 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.372684391 + -0.25 x = -3.372684391 + -0.25 Combine like terms: -3.372684391 + -0.25 = -3.622684391 x = -3.622684391 Simplifying x = -3.622684391Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.122684391, -3.622684391}
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