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Simplifying (y * y) + -5y + -19 = 6y + 1 Multiply y * y (y2) + -5y + -19 = 6y + 1 y2 + -5y + -19 = 6y + 1 Reorder the terms: -19 + -5y + y2 = 6y + 1 Reorder the terms: -19 + -5y + y2 = 1 + 6y Solving -19 + -5y + y2 = 1 + 6y Solving for variable 'y'. Reorder the terms: -19 + -1 + -5y + -6y + y2 = 1 + 6y + -1 + -6y Combine like terms: -19 + -1 = -20 -20 + -5y + -6y + y2 = 1 + 6y + -1 + -6y Combine like terms: -5y + -6y = -11y -20 + -11y + y2 = 1 + 6y + -1 + -6y Reorder the terms: -20 + -11y + y2 = 1 + -1 + 6y + -6y Combine like terms: 1 + -1 = 0 -20 + -11y + y2 = 0 + 6y + -6y -20 + -11y + y2 = 6y + -6y Combine like terms: 6y + -6y = 0 -20 + -11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -11y + 20 + y2 = 0 + 20 Reorder the terms: -20 + 20 + -11y + y2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -11y + y2 = 0 + 20 -11y + y2 = 0 + 20 Combine like terms: 0 + 20 = 20 -11y + y2 = 20 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = 20 + 30.25 Reorder the terms: 30.25 + -11y + y2 = 20 + 30.25 Combine like terms: 20 + 30.25 = 50.25 30.25 + -11y + y2 = 50.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (y + -5.5) equal to 7.088723439 and -7.088723439.Subproblem 1
y + -5.5 = 7.088723439 Simplifying y + -5.5 = 7.088723439 Reorder the terms: -5.5 + y = 7.088723439 Solving -5.5 + y = 7.088723439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 7.088723439 + 5.5 y = 7.088723439 + 5.5 Combine like terms: 7.088723439 + 5.5 = 12.588723439 y = 12.588723439 Simplifying y = 12.588723439Subproblem 2
y + -5.5 = -7.088723439 Simplifying y + -5.5 = -7.088723439 Reorder the terms: -5.5 + y = -7.088723439 Solving -5.5 + y = -7.088723439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -7.088723439 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -7.088723439 + 5.5 y = -7.088723439 + 5.5 Combine like terms: -7.088723439 + 5.5 = -1.588723439 y = -1.588723439 Simplifying y = -1.588723439Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.588723439, -1.588723439}
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