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Simplifying 16x2 + -17x + -80 = 0 Reorder the terms: -80 + -17x + 16x2 = 0 Solving -80 + -17x + 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'. -5 + -1.0625x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.0625x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1.0625x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.0625x + x2 = 0 + 5 -1.0625x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.0625x + x2 = 5 The x term is -1.0625x. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625x + 0.2822265625 + x2 = 5 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625x + x2 = 5 + 0.2822265625 Combine like terms: 5 + 0.2822265625 = 5.2822265625 0.2822265625 + -1.0625x + x2 = 5.2822265625 Factor a perfect square on the left side: (x + -0.53125)(x + -0.53125) = 5.2822265625 Calculate the square root of the right side: 2.298309501 Break this problem into two subproblems by setting (x + -0.53125) equal to 2.298309501 and -2.298309501.Subproblem 1
x + -0.53125 = 2.298309501 Simplifying x + -0.53125 = 2.298309501 Reorder the terms: -0.53125 + x = 2.298309501 Solving -0.53125 + x = 2.298309501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = 2.298309501 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = 2.298309501 + 0.53125 x = 2.298309501 + 0.53125 Combine like terms: 2.298309501 + 0.53125 = 2.829559501 x = 2.829559501 Simplifying x = 2.829559501Subproblem 2
x + -0.53125 = -2.298309501 Simplifying x + -0.53125 = -2.298309501 Reorder the terms: -0.53125 + x = -2.298309501 Solving -0.53125 + x = -2.298309501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = -2.298309501 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = -2.298309501 + 0.53125 x = -2.298309501 + 0.53125 Combine like terms: -2.298309501 + 0.53125 = -1.767059501 x = -1.767059501 Simplifying x = -1.767059501Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.829559501, -1.767059501}
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