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Simplifying 0 = -50x2 + 25x + 1 Reorder the terms: 0 = 1 + 25x + -50x2 Solving 0 = 1 + 25x + -50x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -25x + 50x2 = 1 + 25x + -50x2 + -1 + -25x + 50x2 Reorder the terms: -1 + -25x + 50x2 = 1 + -1 + 25x + -25x + -50x2 + 50x2 Combine like terms: 1 + -1 = 0 -1 + -25x + 50x2 = 0 + 25x + -25x + -50x2 + 50x2 -1 + -25x + 50x2 = 25x + -25x + -50x2 + 50x2 Combine like terms: 25x + -25x = 0 -1 + -25x + 50x2 = 0 + -50x2 + 50x2 -1 + -25x + 50x2 = -50x2 + 50x2 Combine like terms: -50x2 + 50x2 = 0 -1 + -25x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.02 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + -0.5x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + -0.5x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + -0.5x + x2 = 0 + 0.02 -0.5x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 -0.5x + x2 = 0.02 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.02 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.02 + 0.0625 Combine like terms: 0.02 + 0.0625 = 0.0825 0.0625 + -0.5x + x2 = 0.0825 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.0825 Calculate the square root of the right side: 0.287228132 Break this problem into two subproblems by setting (x + -0.25) equal to 0.287228132 and -0.287228132.Subproblem 1
x + -0.25 = 0.287228132 Simplifying x + -0.25 = 0.287228132 Reorder the terms: -0.25 + x = 0.287228132 Solving -0.25 + x = 0.287228132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.287228132 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.287228132 + 0.25 x = 0.287228132 + 0.25 Combine like terms: 0.287228132 + 0.25 = 0.537228132 x = 0.537228132 Simplifying x = 0.537228132Subproblem 2
x + -0.25 = -0.287228132 Simplifying x + -0.25 = -0.287228132 Reorder the terms: -0.25 + x = -0.287228132 Solving -0.25 + x = -0.287228132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.287228132 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.287228132 + 0.25 x = -0.287228132 + 0.25 Combine like terms: -0.287228132 + 0.25 = -0.037228132 x = -0.037228132 Simplifying x = -0.037228132Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.537228132, -0.037228132}
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