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Simplifying -16x2 + 73x + 5 = 0 Reorder the terms: 5 + 73x + -16x2 = 0 Solving 5 + 73x + -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'. -0.3125 + -4.5625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -4.5625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -4.5625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -4.5625x + x2 = 0 + 0.3125 -4.5625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -4.5625x + x2 = 0.3125 The x term is -4.5625x. Take half its coefficient (-2.28125). Square it (5.204101563) and add it to both sides. Add '5.204101563' to each side of the equation. -4.5625x + 5.204101563 + x2 = 0.3125 + 5.204101563 Reorder the terms: 5.204101563 + -4.5625x + x2 = 0.3125 + 5.204101563 Combine like terms: 0.3125 + 5.204101563 = 5.516601563 5.204101563 + -4.5625x + x2 = 5.516601563 Factor a perfect square on the left side: (x + -2.28125)(x + -2.28125) = 5.516601563 Calculate the square root of the right side: 2.348744678 Break this problem into two subproblems by setting (x + -2.28125) equal to 2.348744678 and -2.348744678.Subproblem 1
x + -2.28125 = 2.348744678 Simplifying x + -2.28125 = 2.348744678 Reorder the terms: -2.28125 + x = 2.348744678 Solving -2.28125 + x = 2.348744678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.28125' to each side of the equation. -2.28125 + 2.28125 + x = 2.348744678 + 2.28125 Combine like terms: -2.28125 + 2.28125 = 0.00000 0.00000 + x = 2.348744678 + 2.28125 x = 2.348744678 + 2.28125 Combine like terms: 2.348744678 + 2.28125 = 4.629994678 x = 4.629994678 Simplifying x = 4.629994678Subproblem 2
x + -2.28125 = -2.348744678 Simplifying x + -2.28125 = -2.348744678 Reorder the terms: -2.28125 + x = -2.348744678 Solving -2.28125 + x = -2.348744678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.28125' to each side of the equation. -2.28125 + 2.28125 + x = -2.348744678 + 2.28125 Combine like terms: -2.28125 + 2.28125 = 0.00000 0.00000 + x = -2.348744678 + 2.28125 x = -2.348744678 + 2.28125 Combine like terms: -2.348744678 + 2.28125 = -0.067494678 x = -0.067494678 Simplifying x = -0.067494678Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.629994678, -0.067494678}
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