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Simplifying -25x = -2x2 + 20 Reorder the terms: -25x = 20 + -2x2 Solving -25x = 20 + -2x2 Solving for variable 'x'. Reorder the terms: -20 + -25x + 2x2 = 20 + -2x2 + -20 + 2x2 Reorder the terms: -20 + -25x + 2x2 = 20 + -20 + -2x2 + 2x2 Combine like terms: 20 + -20 = 0 -20 + -25x + 2x2 = 0 + -2x2 + 2x2 -20 + -25x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -20 + -25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -12.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -12.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -12.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12.5x + x2 = 0 + 10 -12.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12.5x + x2 = 10 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 = 10 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 10 + 39.0625 Combine like terms: 10 + 39.0625 = 49.0625 39.0625 + -12.5x + x2 = 49.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 49.0625 Calculate the square root of the right side: 7.004462863 Break this problem into two subproblems by setting (x + -6.25) equal to 7.004462863 and -7.004462863.Subproblem 1
x + -6.25 = 7.004462863 Simplifying x + -6.25 = 7.004462863 Reorder the terms: -6.25 + x = 7.004462863 Solving -6.25 + x = 7.004462863 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 = 7.004462863 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.004462863 + 6.25 x = 7.004462863 + 6.25 Combine like terms: 7.004462863 + 6.25 = 13.254462863 x = 13.254462863 Simplifying x = 13.254462863Subproblem 2
x + -6.25 = -7.004462863 Simplifying x + -6.25 = -7.004462863 Reorder the terms: -6.25 + x = -7.004462863 Solving -6.25 + x = -7.004462863 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 = -7.004462863 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.004462863 + 6.25 x = -7.004462863 + 6.25 Combine like terms: -7.004462863 + 6.25 = -0.754462863 x = -0.754462863 Simplifying x = -0.754462863Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.254462863, -0.754462863}
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