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Simplifying 16x2 + -193x + -576 = 0 Reorder the terms: -576 + -193x + 16x2 = 0 Solving -576 + -193x + 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'. -36 + -12.0625x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -12.0625x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -12.0625x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -12.0625x + x2 = 0 + 36 -12.0625x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -12.0625x + x2 = 36 The x term is -12.0625x. Take half its coefficient (-6.03125). Square it (36.37597656) and add it to both sides. Add '36.37597656' to each side of the equation. -12.0625x + 36.37597656 + x2 = 36 + 36.37597656 Reorder the terms: 36.37597656 + -12.0625x + x2 = 36 + 36.37597656 Combine like terms: 36 + 36.37597656 = 72.37597656 36.37597656 + -12.0625x + x2 = 72.37597656 Factor a perfect square on the left side: (x + -6.03125)(x + -6.03125) = 72.37597656 Calculate the square root of the right side: 8.507407158 Break this problem into two subproblems by setting (x + -6.03125) equal to 8.507407158 and -8.507407158.Subproblem 1
x + -6.03125 = 8.507407158 Simplifying x + -6.03125 = 8.507407158 Reorder the terms: -6.03125 + x = 8.507407158 Solving -6.03125 + x = 8.507407158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.03125' to each side of the equation. -6.03125 + 6.03125 + x = 8.507407158 + 6.03125 Combine like terms: -6.03125 + 6.03125 = 0.00000 0.00000 + x = 8.507407158 + 6.03125 x = 8.507407158 + 6.03125 Combine like terms: 8.507407158 + 6.03125 = 14.538657158 x = 14.538657158 Simplifying x = 14.538657158Subproblem 2
x + -6.03125 = -8.507407158 Simplifying x + -6.03125 = -8.507407158 Reorder the terms: -6.03125 + x = -8.507407158 Solving -6.03125 + x = -8.507407158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.03125' to each side of the equation. -6.03125 + 6.03125 + x = -8.507407158 + 6.03125 Combine like terms: -6.03125 + 6.03125 = 0.00000 0.00000 + x = -8.507407158 + 6.03125 x = -8.507407158 + 6.03125 Combine like terms: -8.507407158 + 6.03125 = -2.476157158 x = -2.476157158 Simplifying x = -2.476157158Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.538657158, -2.476157158}
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