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Simplifying -1Y2 + -10Y + 19 = 0 Reorder the terms: 19 + -10Y + -1Y2 = 0 Solving 19 + -10Y + -1Y2 = 0 Solving for variable 'Y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -19 + 10Y + Y2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + 10Y + 19 + Y2 = 0 + 19 Reorder the terms: -19 + 19 + 10Y + Y2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 10Y + Y2 = 0 + 19 10Y + Y2 = 0 + 19 Combine like terms: 0 + 19 = 19 10Y + Y2 = 19 The Y term is 10Y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10Y + 25 + Y2 = 19 + 25 Reorder the terms: 25 + 10Y + Y2 = 19 + 25 Combine like terms: 19 + 25 = 44 25 + 10Y + Y2 = 44 Factor a perfect square on the left side: (Y + 5)(Y + 5) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (Y + 5) equal to 6.633249581 and -6.633249581.Subproblem 1
Y + 5 = 6.633249581 Simplifying Y + 5 = 6.633249581 Reorder the terms: 5 + Y = 6.633249581 Solving 5 + Y = 6.633249581 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + Y = 6.633249581 + -5 Combine like terms: 5 + -5 = 0 0 + Y = 6.633249581 + -5 Y = 6.633249581 + -5 Combine like terms: 6.633249581 + -5 = 1.633249581 Y = 1.633249581 Simplifying Y = 1.633249581Subproblem 2
Y + 5 = -6.633249581 Simplifying Y + 5 = -6.633249581 Reorder the terms: 5 + Y = -6.633249581 Solving 5 + Y = -6.633249581 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + Y = -6.633249581 + -5 Combine like terms: 5 + -5 = 0 0 + Y = -6.633249581 + -5 Y = -6.633249581 + -5 Combine like terms: -6.633249581 + -5 = -11.633249581 Y = -11.633249581 Simplifying Y = -11.633249581Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.633249581, -11.633249581}
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