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Simplifying 2X2 + -25X = 1 Reorder the terms: -25X + 2X2 = 1 Solving -25X + 2X2 = 1 Solving for variable 'X'. Reorder the terms: -1 + -25X + 2X2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -25X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -12.5X + X2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -12.5X + 0.5 + X2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -12.5X + X2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -12.5X + X2 = 0 + 0.5 -12.5X + X2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -12.5X + X2 = 0.5 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 = 0.5 + 39.0625 Reorder the terms: 39.0625 + -12.5X + X2 = 0.5 + 39.0625 Combine like terms: 0.5 + 39.0625 = 39.5625 39.0625 + -12.5X + X2 = 39.5625 Factor a perfect square on the left side: (X + -6.25)(X + -6.25) = 39.5625 Calculate the square root of the right side: 6.289872813 Break this problem into two subproblems by setting (X + -6.25) equal to 6.289872813 and -6.289872813.Subproblem 1
X + -6.25 = 6.289872813 Simplifying X + -6.25 = 6.289872813 Reorder the terms: -6.25 + X = 6.289872813 Solving -6.25 + X = 6.289872813 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 = 6.289872813 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + X = 6.289872813 + 6.25 X = 6.289872813 + 6.25 Combine like terms: 6.289872813 + 6.25 = 12.539872813 X = 12.539872813 Simplifying X = 12.539872813Subproblem 2
X + -6.25 = -6.289872813 Simplifying X + -6.25 = -6.289872813 Reorder the terms: -6.25 + X = -6.289872813 Solving -6.25 + X = -6.289872813 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 = -6.289872813 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + X = -6.289872813 + 6.25 X = -6.289872813 + 6.25 Combine like terms: -6.289872813 + 6.25 = -0.039872813 X = -0.039872813 Simplifying X = -0.039872813Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.539872813, -0.039872813}
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