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Simplifying 4.9x2 + -16x + -3 = 0 Reorder the terms: -3 + -16x + 4.9x2 = 0 Solving -3 + -16x + 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'. -0.612244898 + -3.265306122x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -3.265306122x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -3.265306122x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -3.265306122x + x2 = 0 + 0.612244898 -3.265306122x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -3.265306122x + x2 = 0.612244898 The x term is -3.265306122x. Take half its coefficient (-1.632653061). Square it (2.665556018) and add it to both sides. Add '2.665556018' to each side of the equation. -3.265306122x + 2.665556018 + x2 = 0.612244898 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122x + x2 = 0.612244898 + 2.665556018 Combine like terms: 0.612244898 + 2.665556018 = 3.277800916 2.665556018 + -3.265306122x + x2 = 3.277800916 Factor a perfect square on the left side: (x + -1.632653061)(x + -1.632653061) = 3.277800916 Calculate the square root of the right side: 1.810469805 Break this problem into two subproblems by setting (x + -1.632653061) equal to 1.810469805 and -1.810469805.Subproblem 1
x + -1.632653061 = 1.810469805 Simplifying x + -1.632653061 = 1.810469805 Reorder the terms: -1.632653061 + x = 1.810469805 Solving -1.632653061 + x = 1.810469805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + x = 1.810469805 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = 1.810469805 + 1.632653061 x = 1.810469805 + 1.632653061 Combine like terms: 1.810469805 + 1.632653061 = 3.443122866 x = 3.443122866 Simplifying x = 3.443122866Subproblem 2
x + -1.632653061 = -1.810469805 Simplifying x + -1.632653061 = -1.810469805 Reorder the terms: -1.632653061 + x = -1.810469805 Solving -1.632653061 + x = -1.810469805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.632653061' to each side of the equation. -1.632653061 + 1.632653061 + x = -1.810469805 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = -1.810469805 + 1.632653061 x = -1.810469805 + 1.632653061 Combine like terms: -1.810469805 + 1.632653061 = -0.177816744 x = -0.177816744 Simplifying x = -0.177816744Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.443122866, -0.177816744}
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