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Simplifying 20x2 + 9x + -1 = 0 Reorder the terms: -1 + 9x + 20x2 = 0 Solving -1 + 9x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.05 + 0.45x + x2 = 0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + 0.45x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + 0.45x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + 0.45x + x2 = 0 + 0.05 0.45x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 0.45x + x2 = 0.05 The x term is 0.45x. Take half its coefficient (0.225). Square it (0.050625) and add it to both sides. Add '0.050625' to each side of the equation. 0.45x + 0.050625 + x2 = 0.05 + 0.050625 Reorder the terms: 0.050625 + 0.45x + x2 = 0.05 + 0.050625 Combine like terms: 0.05 + 0.050625 = 0.100625 0.050625 + 0.45x + x2 = 0.100625 Factor a perfect square on the left side: (x + 0.225)(x + 0.225) = 0.100625 Calculate the square root of the right side: 0.317214439 Break this problem into two subproblems by setting (x + 0.225) equal to 0.317214439 and -0.317214439.Subproblem 1
x + 0.225 = 0.317214439 Simplifying x + 0.225 = 0.317214439 Reorder the terms: 0.225 + x = 0.317214439 Solving 0.225 + x = 0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = 0.317214439 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = 0.317214439 + -0.225 x = 0.317214439 + -0.225 Combine like terms: 0.317214439 + -0.225 = 0.092214439 x = 0.092214439 Simplifying x = 0.092214439Subproblem 2
x + 0.225 = -0.317214439 Simplifying x + 0.225 = -0.317214439 Reorder the terms: 0.225 + x = -0.317214439 Solving 0.225 + x = -0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.225' to each side of the equation. 0.225 + -0.225 + x = -0.317214439 + -0.225 Combine like terms: 0.225 + -0.225 = 0.000 0.000 + x = -0.317214439 + -0.225 x = -0.317214439 + -0.225 Combine like terms: -0.317214439 + -0.225 = -0.542214439 x = -0.542214439 Simplifying x = -0.542214439Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.092214439, -0.542214439}
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