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Simplifying 5y2 + -11y + -22 = 0 Reorder the terms: -22 + -11y + 5y2 = 0 Solving -22 + -11y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + -2.2y + y2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + -2.2y + 4.4 + y2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + -2.2y + y2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + -2.2y + y2 = 0 + 4.4 -2.2y + y2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 -2.2y + y2 = 4.4 The y term is -2.2y. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2y + 1.21 + y2 = 4.4 + 1.21 Reorder the terms: 1.21 + -2.2y + y2 = 4.4 + 1.21 Combine like terms: 4.4 + 1.21 = 5.61 1.21 + -2.2y + y2 = 5.61 Factor a perfect square on the left side: (y + -1.1)(y + -1.1) = 5.61 Calculate the square root of the right side: 2.368543856 Break this problem into two subproblems by setting (y + -1.1) equal to 2.368543856 and -2.368543856.Subproblem 1
y + -1.1 = 2.368543856 Simplifying y + -1.1 = 2.368543856 Reorder the terms: -1.1 + y = 2.368543856 Solving -1.1 + y = 2.368543856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = 2.368543856 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = 2.368543856 + 1.1 y = 2.368543856 + 1.1 Combine like terms: 2.368543856 + 1.1 = 3.468543856 y = 3.468543856 Simplifying y = 3.468543856Subproblem 2
y + -1.1 = -2.368543856 Simplifying y + -1.1 = -2.368543856 Reorder the terms: -1.1 + y = -2.368543856 Solving -1.1 + y = -2.368543856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + y = -2.368543856 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + y = -2.368543856 + 1.1 y = -2.368543856 + 1.1 Combine like terms: -2.368543856 + 1.1 = -1.268543856 y = -1.268543856 Simplifying y = -1.268543856Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.468543856, -1.268543856}
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