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Simplifying 4x2 + -50x + -205 = 0 Reorder the terms: -205 + -50x + 4x2 = 0 Solving -205 + -50x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -51.25 + -12.5x + x2 = 0 Move the constant term to the right: Add '51.25' to each side of the equation. -51.25 + -12.5x + 51.25 + x2 = 0 + 51.25 Reorder the terms: -51.25 + 51.25 + -12.5x + x2 = 0 + 51.25 Combine like terms: -51.25 + 51.25 = 0.00 0.00 + -12.5x + x2 = 0 + 51.25 -12.5x + x2 = 0 + 51.25 Combine like terms: 0 + 51.25 = 51.25 -12.5x + x2 = 51.25 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 51.25 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 51.25 + 39.0625 Combine like terms: 51.25 + 39.0625 = 90.3125 39.0625 + -12.5x + x2 = 90.3125 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 90.3125 Calculate the square root of the right side: 9.503288904 Break this problem into two subproblems by setting (x + -6.25) equal to 9.503288904 and -9.503288904.Subproblem 1
x + -6.25 = 9.503288904 Simplifying x + -6.25 = 9.503288904 Reorder the terms: -6.25 + x = 9.503288904 Solving -6.25 + x = 9.503288904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 9.503288904 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 9.503288904 + 6.25 x = 9.503288904 + 6.25 Combine like terms: 9.503288904 + 6.25 = 15.753288904 x = 15.753288904 Simplifying x = 15.753288904Subproblem 2
x + -6.25 = -9.503288904 Simplifying x + -6.25 = -9.503288904 Reorder the terms: -6.25 + x = -9.503288904 Solving -6.25 + x = -9.503288904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -9.503288904 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -9.503288904 + 6.25 x = -9.503288904 + 6.25 Combine like terms: -9.503288904 + 6.25 = -3.253288904 x = -3.253288904 Simplifying x = -3.253288904Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.753288904, -3.253288904}
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