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Simplifying 2x2 + 10x = 1 Reorder the terms: 10x + 2x2 = 1 Solving 10x + 2x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 10x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 5x + x2 = 0 + 0.5 5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 5x + x2 = 0.5 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.5 + 6.25 Combine like terms: 0.5 + 6.25 = 6.75 6.25 + 5x + x2 = 6.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + 2.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + 2.5 = 2.598076211 Simplifying x + 2.5 = 2.598076211 Reorder the terms: 2.5 + x = 2.598076211 Solving 2.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.598076211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.598076211 + -2.5 x = 2.598076211 + -2.5 Combine like terms: 2.598076211 + -2.5 = 0.098076211 x = 0.098076211 Simplifying x = 0.098076211Subproblem 2
x + 2.5 = -2.598076211 Simplifying x + 2.5 = -2.598076211 Reorder the terms: 2.5 + x = -2.598076211 Solving 2.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.598076211 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.598076211 + -2.5 x = -2.598076211 + -2.5 Combine like terms: -2.598076211 + -2.5 = -5.098076211 x = -5.098076211 Simplifying x = -5.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.098076211, -5.098076211}
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