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Simplifying 25x2 + 50x + 2 = 0 Reorder the terms: 2 + 50x + 25x2 = 0 Solving 2 + 50x + 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'. 0.08 + 2x + x2 = 0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + 2x + -0.08 + x2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + 2x + x2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + 2x + x2 = 0 + -0.08 2x + x2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 2x + x2 = -0.08 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.08 + 1 Reorder the terms: 1 + 2x + x2 = -0.08 + 1 Combine like terms: -0.08 + 1 = 0.92 1 + 2x + x2 = 0.92 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.92 Calculate the square root of the right side: 0.959166305 Break this problem into two subproblems by setting (x + 1) equal to 0.959166305 and -0.959166305.Subproblem 1
x + 1 = 0.959166305 Simplifying x + 1 = 0.959166305 Reorder the terms: 1 + x = 0.959166305 Solving 1 + x = 0.959166305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.959166305 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.959166305 + -1 x = 0.959166305 + -1 Combine like terms: 0.959166305 + -1 = -0.040833695 x = -0.040833695 Simplifying x = -0.040833695Subproblem 2
x + 1 = -0.959166305 Simplifying x + 1 = -0.959166305 Reorder the terms: 1 + x = -0.959166305 Solving 1 + x = -0.959166305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.959166305 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.959166305 + -1 x = -0.959166305 + -1 Combine like terms: -0.959166305 + -1 = -1.959166305 x = -1.959166305 Simplifying x = -1.959166305Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.040833695, -1.959166305}
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