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Simplifying 20x2 + 17x + -20 = 0 Reorder the terms: -20 + 17x + 20x2 = 0 Solving -20 + 17x + 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'. -1 + 0.85x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.85x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.85x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.85x + x2 = 0 + 1 0.85x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.85x + x2 = 1 The x term is 0.85x. Take half its coefficient (0.425). Square it (0.180625) and add it to both sides. Add '0.180625' to each side of the equation. 0.85x + 0.180625 + x2 = 1 + 0.180625 Reorder the terms: 0.180625 + 0.85x + x2 = 1 + 0.180625 Combine like terms: 1 + 0.180625 = 1.180625 0.180625 + 0.85x + x2 = 1.180625 Factor a perfect square on the left side: (x + 0.425)(x + 0.425) = 1.180625 Calculate the square root of the right side: 1.086565691 Break this problem into two subproblems by setting (x + 0.425) equal to 1.086565691 and -1.086565691.Subproblem 1
x + 0.425 = 1.086565691 Simplifying x + 0.425 = 1.086565691 Reorder the terms: 0.425 + x = 1.086565691 Solving 0.425 + x = 1.086565691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.425' to each side of the equation. 0.425 + -0.425 + x = 1.086565691 + -0.425 Combine like terms: 0.425 + -0.425 = 0.000 0.000 + x = 1.086565691 + -0.425 x = 1.086565691 + -0.425 Combine like terms: 1.086565691 + -0.425 = 0.661565691 x = 0.661565691 Simplifying x = 0.661565691Subproblem 2
x + 0.425 = -1.086565691 Simplifying x + 0.425 = -1.086565691 Reorder the terms: 0.425 + x = -1.086565691 Solving 0.425 + x = -1.086565691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.425' to each side of the equation. 0.425 + -0.425 + x = -1.086565691 + -0.425 Combine like terms: 0.425 + -0.425 = 0.000 0.000 + x = -1.086565691 + -0.425 x = -1.086565691 + -0.425 Combine like terms: -1.086565691 + -0.425 = -1.511565691 x = -1.511565691 Simplifying x = -1.511565691Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.661565691, -1.511565691}
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