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Simplifying -1y2 + 19y = 1 Reorder the terms: 19y + -1y2 = 1 Solving 19y + -1y2 = 1 Solving for variable 'y'. Reorder the terms: -1 + 19y + -1y2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 19y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -19y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -19y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -19y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -19y + y2 = 0 + -1 -19y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -19y + y2 = -1 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = -1 + 90.25 Reorder the terms: 90.25 + -19y + y2 = -1 + 90.25 Combine like terms: -1 + 90.25 = 89.25 90.25 + -19y + y2 = 89.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (y + -9.5) equal to 9.447221814 and -9.447221814.Subproblem 1
y + -9.5 = 9.447221814 Simplifying y + -9.5 = 9.447221814 Reorder the terms: -9.5 + y = 9.447221814 Solving -9.5 + y = 9.447221814 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 9.447221814 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 9.447221814 + 9.5 y = 9.447221814 + 9.5 Combine like terms: 9.447221814 + 9.5 = 18.947221814 y = 18.947221814 Simplifying y = 18.947221814Subproblem 2
y + -9.5 = -9.447221814 Simplifying y + -9.5 = -9.447221814 Reorder the terms: -9.5 + y = -9.447221814 Solving -9.5 + y = -9.447221814 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -9.447221814 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -9.447221814 + 9.5 y = -9.447221814 + 9.5 Combine like terms: -9.447221814 + 9.5 = 0.052778186 y = 0.052778186 Simplifying y = 0.052778186Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.947221814, 0.052778186}
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