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Simplifying 25x2 + 50x + -1 = 0 Reorder the terms: -1 + 50x + 25x2 = 0 Solving -1 + 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'. -0.04 + 2x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + 2x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + 2x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + 2x + x2 = 0 + 0.04 2x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 2x + x2 = 0.04 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 = 0.04 + 1 Reorder the terms: 1 + 2x + x2 = 0.04 + 1 Combine like terms: 0.04 + 1 = 1.04 1 + 2x + x2 = 1.04 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.04 Calculate the square root of the right side: 1.019803903 Break this problem into two subproblems by setting (x + 1) equal to 1.019803903 and -1.019803903.Subproblem 1
x + 1 = 1.019803903 Simplifying x + 1 = 1.019803903 Reorder the terms: 1 + x = 1.019803903 Solving 1 + x = 1.019803903 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 = 1.019803903 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.019803903 + -1 x = 1.019803903 + -1 Combine like terms: 1.019803903 + -1 = 0.019803903 x = 0.019803903 Simplifying x = 0.019803903Subproblem 2
x + 1 = -1.019803903 Simplifying x + 1 = -1.019803903 Reorder the terms: 1 + x = -1.019803903 Solving 1 + x = -1.019803903 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 = -1.019803903 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.019803903 + -1 x = -1.019803903 + -1 Combine like terms: -1.019803903 + -1 = -2.019803903 x = -2.019803903 Simplifying x = -2.019803903Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019803903, -2.019803903}
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