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Simplifying 25x2 + -5x + -1 = 0 Reorder the terms: -1 + -5x + 25x2 = 0 Solving -1 + -5x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -0.2x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -0.2x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -0.2x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -0.2x + x2 = 0 + 0.04 -0.2x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -0.2x + x2 = 0.04 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 0.04 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 0.04 + 0.01 Combine like terms: 0.04 + 0.01 = 0.05 0.01 + -0.2x + x2 = 0.05 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 0.05 Calculate the square root of the right side: 0.223606798 Break this problem into two subproblems by setting (x + -0.1) equal to 0.223606798 and -0.223606798.Subproblem 1
x + -0.1 = 0.223606798 Simplifying x + -0.1 = 0.223606798 Reorder the terms: -0.1 + x = 0.223606798 Solving -0.1 + x = 0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0.223606798 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0.223606798 + 0.1 x = 0.223606798 + 0.1 Combine like terms: 0.223606798 + 0.1 = 0.323606798 x = 0.323606798 Simplifying x = 0.323606798Subproblem 2
x + -0.1 = -0.223606798 Simplifying x + -0.1 = -0.223606798 Reorder the terms: -0.1 + x = -0.223606798 Solving -0.1 + x = -0.223606798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -0.223606798 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -0.223606798 + 0.1 x = -0.223606798 + 0.1 Combine like terms: -0.223606798 + 0.1 = -0.123606798 x = -0.123606798 Simplifying x = -0.123606798Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.323606798, -0.123606798}
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