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Simplifying -4.9(x2) + (3.9x) + 1 = 0 Reorder the terms: 1 + (3.9x) + -4.9x2 = 0 Solving 1 + (3.9x) + -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 + (-0.7959183673x) + x2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + (-0.7959183673x) + 0.2040816327 + x2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + (-0.7959183673x) + x2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + (-0.7959183673x) + x2 = 0 + 0.2040816327 (-0.7959183673x) + x2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 (-0.7959183673x) + x2 = 0.2040816327 The x term is (-0.7959183673x). Take half its coefficient (-0.3979591837). Square it (0.1583715119) and add it to both sides. Add '0.1583715119' to each side of the equation. (-0.7959183673x) + 0.1583715119 + x2 = 0.2040816327 + 0.1583715119 Reorder the terms: 0.1583715119 + (-0.7959183673x) + x2 = 0.2040816327 + 0.1583715119 Combine like terms: 0.2040816327 + 0.1583715119 = 0.3624531446 0.1583715119 + (-0.7959183673x) + x2 = 0.3624531446 Factor a perfect square on the left side: (x + -0.3979591837)(x + -0.3979591837) = 0.3624531446 Calculate the square root of the right side: 0.602040816 Break this problem into two subproblems by setting (x + -0.3979591837) equal to 0.602040816 and -0.602040816.Subproblem 1
x + -0.3979591837 = 0.602040816 Simplifying x + -0.3979591837 = 0.602040816 Reorder the terms: -0.3979591837 + x = 0.602040816 Solving -0.3979591837 + x = 0.602040816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + x = 0.602040816 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + x = 0.602040816 + 0.3979591837 x = 0.602040816 + 0.3979591837 Combine like terms: 0.602040816 + 0.3979591837 = 0.9999999997 x = 0.9999999997 Simplifying x = 0.9999999997Subproblem 2
x + -0.3979591837 = -0.602040816 Simplifying x + -0.3979591837 = -0.602040816 Reorder the terms: -0.3979591837 + x = -0.602040816 Solving -0.3979591837 + x = -0.602040816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3979591837' to each side of the equation. -0.3979591837 + 0.3979591837 + x = -0.602040816 + 0.3979591837 Combine like terms: -0.3979591837 + 0.3979591837 = 0.0000000000 0.0000000000 + x = -0.602040816 + 0.3979591837 x = -0.602040816 + 0.3979591837 Combine like terms: -0.602040816 + 0.3979591837 = -0.2040816323 x = -0.2040816323 Simplifying x = -0.2040816323Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9999999997, -0.2040816323}
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