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Simplifying 4.9x2 + -16x + -8 = 0 Reorder the terms: -8 + -16x + 4.9x2 = 0 Solving -8 + -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'. -1.632653061 + -3.265306122x + x2 = 0 Move the constant term to the right: Add '1.632653061' to each side of the equation. -1.632653061 + -3.265306122x + 1.632653061 + x2 = 0 + 1.632653061 Reorder the terms: -1.632653061 + 1.632653061 + -3.265306122x + x2 = 0 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + -3.265306122x + x2 = 0 + 1.632653061 -3.265306122x + x2 = 0 + 1.632653061 Combine like terms: 0 + 1.632653061 = 1.632653061 -3.265306122x + x2 = 1.632653061 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 = 1.632653061 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122x + x2 = 1.632653061 + 2.665556018 Combine like terms: 1.632653061 + 2.665556018 = 4.298209079 2.665556018 + -3.265306122x + x2 = 4.298209079 Factor a perfect square on the left side: (x + -1.632653061)(x + -1.632653061) = 4.298209079 Calculate the square root of the right side: 2.073212261 Break this problem into two subproblems by setting (x + -1.632653061) equal to 2.073212261 and -2.073212261.Subproblem 1
x + -1.632653061 = 2.073212261 Simplifying x + -1.632653061 = 2.073212261 Reorder the terms: -1.632653061 + x = 2.073212261 Solving -1.632653061 + x = 2.073212261 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 = 2.073212261 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = 2.073212261 + 1.632653061 x = 2.073212261 + 1.632653061 Combine like terms: 2.073212261 + 1.632653061 = 3.705865322 x = 3.705865322 Simplifying x = 3.705865322Subproblem 2
x + -1.632653061 = -2.073212261 Simplifying x + -1.632653061 = -2.073212261 Reorder the terms: -1.632653061 + x = -2.073212261 Solving -1.632653061 + x = -2.073212261 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 = -2.073212261 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = -2.073212261 + 1.632653061 x = -2.073212261 + 1.632653061 Combine like terms: -2.073212261 + 1.632653061 = -0.4405592 x = -0.4405592 Simplifying x = -0.4405592Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.705865322, -0.4405592}
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