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Simplifying 4.9x2 + -16x + -10 = 0 Reorder the terms: -10 + -16x + 4.9x2 = 0 Solving -10 + -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'. -2.040816327 + -3.265306122x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -3.265306122x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -3.265306122x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -3.265306122x + x2 = 0 + 2.040816327 -3.265306122x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -3.265306122x + x2 = 2.040816327 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 = 2.040816327 + 2.665556018 Reorder the terms: 2.665556018 + -3.265306122x + x2 = 2.040816327 + 2.665556018 Combine like terms: 2.040816327 + 2.665556018 = 4.706372345 2.665556018 + -3.265306122x + x2 = 4.706372345 Factor a perfect square on the left side: (x + -1.632653061)(x + -1.632653061) = 4.706372345 Calculate the square root of the right side: 2.169417513 Break this problem into two subproblems by setting (x + -1.632653061) equal to 2.169417513 and -2.169417513.Subproblem 1
x + -1.632653061 = 2.169417513 Simplifying x + -1.632653061 = 2.169417513 Reorder the terms: -1.632653061 + x = 2.169417513 Solving -1.632653061 + x = 2.169417513 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 = 2.169417513 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = 2.169417513 + 1.632653061 x = 2.169417513 + 1.632653061 Combine like terms: 2.169417513 + 1.632653061 = 3.802070574 x = 3.802070574 Simplifying x = 3.802070574Subproblem 2
x + -1.632653061 = -2.169417513 Simplifying x + -1.632653061 = -2.169417513 Reorder the terms: -1.632653061 + x = -2.169417513 Solving -1.632653061 + x = -2.169417513 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 = -2.169417513 + 1.632653061 Combine like terms: -1.632653061 + 1.632653061 = 0.000000000 0.000000000 + x = -2.169417513 + 1.632653061 x = -2.169417513 + 1.632653061 Combine like terms: -2.169417513 + 1.632653061 = -0.536764452 x = -0.536764452 Simplifying x = -0.536764452Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.802070574, -0.536764452}
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