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Simplifying 25x2 + 12x + -13 = 11x + -8 + -25x2 Reorder the terms: -13 + 12x + 25x2 = 11x + -8 + -25x2 Reorder the terms: -13 + 12x + 25x2 = -8 + 11x + -25x2 Solving -13 + 12x + 25x2 = -8 + 11x + -25x2 Solving for variable 'x'. Reorder the terms: -13 + 8 + 12x + -11x + 25x2 + 25x2 = -8 + 11x + -25x2 + 8 + -11x + 25x2 Combine like terms: -13 + 8 = -5 -5 + 12x + -11x + 25x2 + 25x2 = -8 + 11x + -25x2 + 8 + -11x + 25x2 Combine like terms: 12x + -11x = 1x -5 + 1x + 25x2 + 25x2 = -8 + 11x + -25x2 + 8 + -11x + 25x2 Combine like terms: 25x2 + 25x2 = 50x2 -5 + 1x + 50x2 = -8 + 11x + -25x2 + 8 + -11x + 25x2 Reorder the terms: -5 + 1x + 50x2 = -8 + 8 + 11x + -11x + -25x2 + 25x2 Combine like terms: -8 + 8 = 0 -5 + 1x + 50x2 = 0 + 11x + -11x + -25x2 + 25x2 -5 + 1x + 50x2 = 11x + -11x + -25x2 + 25x2 Combine like terms: 11x + -11x = 0 -5 + 1x + 50x2 = 0 + -25x2 + 25x2 -5 + 1x + 50x2 = -25x2 + 25x2 Combine like terms: -25x2 + 25x2 = 0 -5 + 1x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.1 + 0.02x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.02x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.02x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.02x + x2 = 0.0 + 0.1 0.02x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.02x + x2 = 0.1 The x term is 0.02x. Take half its coefficient (0.01). Square it (0.0001) and add it to both sides. Add '0.0001' to each side of the equation. 0.02x + 0.0001 + x2 = 0.1 + 0.0001 Reorder the terms: 0.0001 + 0.02x + x2 = 0.1 + 0.0001 Combine like terms: 0.1 + 0.0001 = 0.1001 0.0001 + 0.02x + x2 = 0.1001 Factor a perfect square on the left side: (x + 0.01)(x + 0.01) = 0.1001 Calculate the square root of the right side: 0.31638584 Break this problem into two subproblems by setting (x + 0.01) equal to 0.31638584 and -0.31638584.Subproblem 1
x + 0.01 = 0.31638584 Simplifying x + 0.01 = 0.31638584 Reorder the terms: 0.01 + x = 0.31638584 Solving 0.01 + x = 0.31638584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = 0.31638584 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = 0.31638584 + -0.01 x = 0.31638584 + -0.01 Combine like terms: 0.31638584 + -0.01 = 0.30638584 x = 0.30638584 Simplifying x = 0.30638584Subproblem 2
x + 0.01 = -0.31638584 Simplifying x + 0.01 = -0.31638584 Reorder the terms: 0.01 + x = -0.31638584 Solving 0.01 + x = -0.31638584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01' to each side of the equation. 0.01 + -0.01 + x = -0.31638584 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + x = -0.31638584 + -0.01 x = -0.31638584 + -0.01 Combine like terms: -0.31638584 + -0.01 = -0.32638584 x = -0.32638584 Simplifying x = -0.32638584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.30638584, -0.32638584}
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