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Simplifying 25x2 + 10x = 11 Reorder the terms: 10x + 25x2 = 11 Solving 10x + 25x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 10x + 25x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.44 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.44' to each side of the equation. -0.44 + 0.4x + 0.44 + x2 = 0 + 0.44 Reorder the terms: -0.44 + 0.44 + 0.4x + x2 = 0 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + 0.4x + x2 = 0 + 0.44 0.4x + x2 = 0 + 0.44 Combine like terms: 0 + 0.44 = 0.44 0.4x + x2 = 0.44 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.44 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.44 + 0.04 Combine like terms: 0.44 + 0.04 = 0.48 0.04 + 0.4x + x2 = 0.48 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + 0.2) equal to 0.692820323 and -0.692820323.Subproblem 1
x + 0.2 = 0.692820323 Simplifying x + 0.2 = 0.692820323 Reorder the terms: 0.2 + x = 0.692820323 Solving 0.2 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.692820323 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.692820323 + -0.2 x = 0.692820323 + -0.2 Combine like terms: 0.692820323 + -0.2 = 0.492820323 x = 0.492820323 Simplifying x = 0.492820323Subproblem 2
x + 0.2 = -0.692820323 Simplifying x + 0.2 = -0.692820323 Reorder the terms: 0.2 + x = -0.692820323 Solving 0.2 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.692820323 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.692820323 + -0.2 x = -0.692820323 + -0.2 Combine like terms: -0.692820323 + -0.2 = -0.892820323 x = -0.892820323 Simplifying x = -0.892820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.492820323, -0.892820323}
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