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Simplifying 4.9x2 + 0.4x + -1 = 0 Reorder the terms: -1 + 0.4x + 4.9x2 = 0 Solving -1 + 0.4x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.2040816327 + 0.08163265306x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.08163265306x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + 0.08163265306x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + 0.08163265306x + x2 = 0 + 0.2040816327 0.08163265306x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 0.08163265306x + x2 = 0.2040816327 The x term is 0.08163265306x. Take half its coefficient (0.04081632653). Square it (0.001665972511) and add it to both sides. Add '0.001665972511' to each side of the equation. 0.08163265306x + 0.001665972511 + x2 = 0.2040816327 + 0.001665972511 Reorder the terms: 0.001665972511 + 0.08163265306x + x2 = 0.2040816327 + 0.001665972511 Combine like terms: 0.2040816327 + 0.001665972511 = 0.205747605211 0.001665972511 + 0.08163265306x + x2 = 0.205747605211 Factor a perfect square on the left side: (x + 0.04081632653)(x + 0.04081632653) = 0.205747605211 Calculate the square root of the right side: 0.453594097 Break this problem into two subproblems by setting (x + 0.04081632653) equal to 0.453594097 and -0.453594097.Subproblem 1
x + 0.04081632653 = 0.453594097 Simplifying x + 0.04081632653 = 0.453594097 Reorder the terms: 0.04081632653 + x = 0.453594097 Solving 0.04081632653 + x = 0.453594097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04081632653' to each side of the equation. 0.04081632653 + -0.04081632653 + x = 0.453594097 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + x = 0.453594097 + -0.04081632653 x = 0.453594097 + -0.04081632653 Combine like terms: 0.453594097 + -0.04081632653 = 0.41277777047 x = 0.41277777047 Simplifying x = 0.41277777047Subproblem 2
x + 0.04081632653 = -0.453594097 Simplifying x + 0.04081632653 = -0.453594097 Reorder the terms: 0.04081632653 + x = -0.453594097 Solving 0.04081632653 + x = -0.453594097 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04081632653' to each side of the equation. 0.04081632653 + -0.04081632653 + x = -0.453594097 + -0.04081632653 Combine like terms: 0.04081632653 + -0.04081632653 = 0.00000000000 0.00000000000 + x = -0.453594097 + -0.04081632653 x = -0.453594097 + -0.04081632653 Combine like terms: -0.453594097 + -0.04081632653 = -0.49441042353 x = -0.49441042353 Simplifying x = -0.49441042353Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41277777047, -0.49441042353}
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