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Simplifying 25x2 + 10x = 1 Reorder the terms: 10x + 25x2 = 1 Solving 10x + 25x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 10x + 25x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 0.4x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 0.4x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 0.4x + x2 = 0 + 0.04 0.4x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 0.4x + x2 = 0.04 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 = 0.04 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.04 + 0.04 Combine like terms: 0.04 + 0.04 = 0.08 0.04 + 0.4x + x2 = 0.08 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.08 Calculate the square root of the right side: 0.282842712 Break this problem into two subproblems by setting (x + 0.2) equal to 0.282842712 and -0.282842712.Subproblem 1
x + 0.2 = 0.282842712 Simplifying x + 0.2 = 0.282842712 Reorder the terms: 0.2 + x = 0.282842712 Solving 0.2 + x = 0.282842712 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 = 0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.282842712 + -0.2 x = 0.282842712 + -0.2 Combine like terms: 0.282842712 + -0.2 = 0.082842712 x = 0.082842712 Simplifying x = 0.082842712Subproblem 2
x + 0.2 = -0.282842712 Simplifying x + 0.2 = -0.282842712 Reorder the terms: 0.2 + x = -0.282842712 Solving 0.2 + x = -0.282842712 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 = -0.282842712 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.282842712 + -0.2 x = -0.282842712 + -0.2 Combine like terms: -0.282842712 + -0.2 = -0.482842712 x = -0.482842712 Simplifying x = -0.482842712Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.082842712, -0.482842712}
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