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Simplifying 16x2 + -68x + 27 = 0 Reorder the terms: 27 + -68x + 16x2 = 0 Solving 27 + -68x + 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'. 1.6875 + -4.25x + x2 = 0 Move the constant term to the right: Add '-1.6875' to each side of the equation. 1.6875 + -4.25x + -1.6875 + x2 = 0 + -1.6875 Reorder the terms: 1.6875 + -1.6875 + -4.25x + x2 = 0 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + -4.25x + x2 = 0 + -1.6875 -4.25x + x2 = 0 + -1.6875 Combine like terms: 0 + -1.6875 = -1.6875 -4.25x + x2 = -1.6875 The x term is -4.25x. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25x + 4.515625 + x2 = -1.6875 + 4.515625 Reorder the terms: 4.515625 + -4.25x + x2 = -1.6875 + 4.515625 Combine like terms: -1.6875 + 4.515625 = 2.828125 4.515625 + -4.25x + x2 = 2.828125 Factor a perfect square on the left side: (x + -2.125)(x + -2.125) = 2.828125 Calculate the square root of the right side: 1.681703006 Break this problem into two subproblems by setting (x + -2.125) equal to 1.681703006 and -1.681703006.Subproblem 1
x + -2.125 = 1.681703006 Simplifying x + -2.125 = 1.681703006 Reorder the terms: -2.125 + x = 1.681703006 Solving -2.125 + x = 1.681703006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = 1.681703006 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = 1.681703006 + 2.125 x = 1.681703006 + 2.125 Combine like terms: 1.681703006 + 2.125 = 3.806703006 x = 3.806703006 Simplifying x = 3.806703006Subproblem 2
x + -2.125 = -1.681703006 Simplifying x + -2.125 = -1.681703006 Reorder the terms: -2.125 + x = -1.681703006 Solving -2.125 + x = -1.681703006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + x = -1.681703006 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + x = -1.681703006 + 2.125 x = -1.681703006 + 2.125 Combine like terms: -1.681703006 + 2.125 = 0.443296994 x = 0.443296994 Simplifying x = 0.443296994Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.806703006, 0.443296994}
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