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Simplifying 16x2 + -184x + -33 = 0 Reorder the terms: -33 + -184x + 16x2 = 0 Solving -33 + -184x + 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'. -2.0625 + -11.5x + x2 = 0 Move the constant term to the right: Add '2.0625' to each side of the equation. -2.0625 + -11.5x + 2.0625 + x2 = 0 + 2.0625 Reorder the terms: -2.0625 + 2.0625 + -11.5x + x2 = 0 + 2.0625 Combine like terms: -2.0625 + 2.0625 = 0.0000 0.0000 + -11.5x + x2 = 0 + 2.0625 -11.5x + x2 = 0 + 2.0625 Combine like terms: 0 + 2.0625 = 2.0625 -11.5x + x2 = 2.0625 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 2.0625 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 2.0625 + 33.0625 Combine like terms: 2.0625 + 33.0625 = 35.125 33.0625 + -11.5x + x2 = 35.125 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 35.125 Calculate the square root of the right side: 5.926634796 Break this problem into two subproblems by setting (x + -5.75) equal to 5.926634796 and -5.926634796.Subproblem 1
x + -5.75 = 5.926634796 Simplifying x + -5.75 = 5.926634796 Reorder the terms: -5.75 + x = 5.926634796 Solving -5.75 + x = 5.926634796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 5.926634796 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 5.926634796 + 5.75 x = 5.926634796 + 5.75 Combine like terms: 5.926634796 + 5.75 = 11.676634796 x = 11.676634796 Simplifying x = 11.676634796Subproblem 2
x + -5.75 = -5.926634796 Simplifying x + -5.75 = -5.926634796 Reorder the terms: -5.75 + x = -5.926634796 Solving -5.75 + x = -5.926634796 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -5.926634796 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -5.926634796 + 5.75 x = -5.926634796 + 5.75 Combine like terms: -5.926634796 + 5.75 = -0.176634796 x = -0.176634796 Simplifying x = -0.176634796Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.676634796, -0.176634796}
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