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Simplifying 4.9x2 + 1.414x + -1 = 0 Reorder the terms: -1 + 1.414x + 4.9x2 = 0 Solving -1 + 1.414x + 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 + 0.2885714286x + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2885714286x + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + 0.2885714286x + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + 0.2885714286x + x2 = 0 + 0.2040816327 0.2885714286x + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 0.2885714286x + x2 = 0.2040816327 The x term is 0.2885714286x. Take half its coefficient (0.1442857143). Square it (0.02081836735) and add it to both sides. Add '0.02081836735' to each side of the equation. 0.2885714286x + 0.02081836735 + x2 = 0.2040816327 + 0.02081836735 Reorder the terms: 0.02081836735 + 0.2885714286x + x2 = 0.2040816327 + 0.02081836735 Combine like terms: 0.2040816327 + 0.02081836735 = 0.22490000005 0.02081836735 + 0.2885714286x + x2 = 0.22490000005 Factor a perfect square on the left side: (x + 0.1442857143)(x + 0.1442857143) = 0.22490000005 Calculate the square root of the right side: 0.474236228 Break this problem into two subproblems by setting (x + 0.1442857143) equal to 0.474236228 and -0.474236228.Subproblem 1
x + 0.1442857143 = 0.474236228 Simplifying x + 0.1442857143 = 0.474236228 Reorder the terms: 0.1442857143 + x = 0.474236228 Solving 0.1442857143 + x = 0.474236228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1442857143' to each side of the equation. 0.1442857143 + -0.1442857143 + x = 0.474236228 + -0.1442857143 Combine like terms: 0.1442857143 + -0.1442857143 = 0.0000000000 0.0000000000 + x = 0.474236228 + -0.1442857143 x = 0.474236228 + -0.1442857143 Combine like terms: 0.474236228 + -0.1442857143 = 0.3299505137 x = 0.3299505137 Simplifying x = 0.3299505137Subproblem 2
x + 0.1442857143 = -0.474236228 Simplifying x + 0.1442857143 = -0.474236228 Reorder the terms: 0.1442857143 + x = -0.474236228 Solving 0.1442857143 + x = -0.474236228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1442857143' to each side of the equation. 0.1442857143 + -0.1442857143 + x = -0.474236228 + -0.1442857143 Combine like terms: 0.1442857143 + -0.1442857143 = 0.0000000000 0.0000000000 + x = -0.474236228 + -0.1442857143 x = -0.474236228 + -0.1442857143 Combine like terms: -0.474236228 + -0.1442857143 = -0.6185219423 x = -0.6185219423 Simplifying x = -0.6185219423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3299505137, -0.6185219423}
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