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Simplifying 2x2 + -11 = -25x Reorder the terms: -11 + 2x2 = -25x Solving -11 + 2x2 = -25x Solving for variable 'x'. Reorder the terms: -11 + 25x + 2x2 = -25x + 25x Combine like terms: -25x + 25x = 0 -11 + 25x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5.5 + 12.5x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 12.5x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 12.5x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 12.5x + x2 = 0 + 5.5 12.5x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 12.5x + x2 = 5.5 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 = 5.5 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 5.5 + 39.0625 Combine like terms: 5.5 + 39.0625 = 44.5625 39.0625 + 12.5x + x2 = 44.5625 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 44.5625 Calculate the square root of the right side: 6.675514961 Break this problem into two subproblems by setting (x + 6.25) equal to 6.675514961 and -6.675514961.Subproblem 1
x + 6.25 = 6.675514961 Simplifying x + 6.25 = 6.675514961 Reorder the terms: 6.25 + x = 6.675514961 Solving 6.25 + x = 6.675514961 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 = 6.675514961 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.675514961 + -6.25 x = 6.675514961 + -6.25 Combine like terms: 6.675514961 + -6.25 = 0.425514961 x = 0.425514961 Simplifying x = 0.425514961Subproblem 2
x + 6.25 = -6.675514961 Simplifying x + 6.25 = -6.675514961 Reorder the terms: 6.25 + x = -6.675514961 Solving 6.25 + x = -6.675514961 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 = -6.675514961 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.675514961 + -6.25 x = -6.675514961 + -6.25 Combine like terms: -6.675514961 + -6.25 = -12.925514961 x = -12.925514961 Simplifying x = -12.925514961Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.425514961, -12.925514961}
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