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Simplifying -4.9x2 + 16x + 1.5 = 0 Reorder the terms: 1.5 + 16x + -4.9x2 = 0 Solving 1.5 + 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'. -0.306122449 + -3.265306122x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -3.265306122x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -3.265306122x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -3.265306122x + x2 = 0 + 0.306122449 -3.265306122x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -3.265306122x + x2 = 0.306122449 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 = 0.306122449 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122x + x2 = 0.306122449 + 2.665556018 Combine like terms: 0.306122449 + 2.665556018 = 2.971678467 2.665556018 + -3.265306122x + x2 = 2.971678467 Factor a perfect square on the left side: (x + -1.632653061)(x + -1.632653061) = 2.971678467 Calculate the square root of the right side: 1.723855698 Break this problem into two subproblems by setting (x + -1.632653061) equal to 1.723855698 and -1.723855698.Subproblem 1
x + -1.632653061 = 1.723855698 Simplifying x + -1.632653061 = 1.723855698 Reorder the terms: -1.632653061 + x = 1.723855698 Solving -1.632653061 + x = 1.723855698 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 = 1.723855698 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = 1.723855698 + 1.632653061 x = 1.723855698 + 1.632653061 Combine like terms: 1.723855698 + 1.632653061 = 3.356508759 x = 3.356508759 Simplifying x = 3.356508759Subproblem 2
x + -1.632653061 = -1.723855698 Simplifying x + -1.632653061 = -1.723855698 Reorder the terms: -1.632653061 + x = -1.723855698 Solving -1.632653061 + x = -1.723855698 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 = -1.723855698 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = -1.723855698 + 1.632653061 x = -1.723855698 + 1.632653061 Combine like terms: -1.723855698 + 1.632653061 = -0.091202637 x = -0.091202637 Simplifying x = -0.091202637Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.356508759, -0.091202637}
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