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Simplifying 5x2 + -25x + 1 = 0 Reorder the terms: 1 + -25x + 5x2 = 0 Solving 1 + -25x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -5x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -5x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -5x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -5x + x2 = 0 + -0.2 -5x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -5x + x2 = -0.2 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 = -0.2 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -0.2 + 6.25 Combine like terms: -0.2 + 6.25 = 6.05 6.25 + -5x + x2 = 6.05 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.05 Calculate the square root of the right side: 2.459674775 Break this problem into two subproblems by setting (x + -2.5) equal to 2.459674775 and -2.459674775.Subproblem 1
x + -2.5 = 2.459674775 Simplifying x + -2.5 = 2.459674775 Reorder the terms: -2.5 + x = 2.459674775 Solving -2.5 + x = 2.459674775 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 = 2.459674775 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.459674775 + 2.5 x = 2.459674775 + 2.5 Combine like terms: 2.459674775 + 2.5 = 4.959674775 x = 4.959674775 Simplifying x = 4.959674775Subproblem 2
x + -2.5 = -2.459674775 Simplifying x + -2.5 = -2.459674775 Reorder the terms: -2.5 + x = -2.459674775 Solving -2.5 + x = -2.459674775 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 = -2.459674775 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.459674775 + 2.5 x = -2.459674775 + 2.5 Combine like terms: -2.459674775 + 2.5 = 0.040325225 x = 0.040325225 Simplifying x = 0.040325225Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.959674775, 0.040325225}
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