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Simplifying 5y2 + -8y + -11 = 0 Reorder the terms: -11 + -8y + 5y2 = 0 Solving -11 + -8y + 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'. -2.2 + -1.6y + y2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -1.6y + 2.2 + y2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -1.6y + y2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -1.6y + y2 = 0 + 2.2 -1.6y + y2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -1.6y + y2 = 2.2 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = 2.2 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = 2.2 + 0.64 Combine like terms: 2.2 + 0.64 = 2.84 0.64 + -1.6y + y2 = 2.84 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = 2.84 Calculate the square root of the right side: 1.685229955 Break this problem into two subproblems by setting (y + -0.8) equal to 1.685229955 and -1.685229955.Subproblem 1
y + -0.8 = 1.685229955 Simplifying y + -0.8 = 1.685229955 Reorder the terms: -0.8 + y = 1.685229955 Solving -0.8 + y = 1.685229955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = 1.685229955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = 1.685229955 + 0.8 y = 1.685229955 + 0.8 Combine like terms: 1.685229955 + 0.8 = 2.485229955 y = 2.485229955 Simplifying y = 2.485229955Subproblem 2
y + -0.8 = -1.685229955 Simplifying y + -0.8 = -1.685229955 Reorder the terms: -0.8 + y = -1.685229955 Solving -0.8 + y = -1.685229955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + y = -1.685229955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + y = -1.685229955 + 0.8 y = -1.685229955 + 0.8 Combine like terms: -1.685229955 + 0.8 = -0.885229955 y = -0.885229955 Simplifying y = -0.885229955Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.485229955, -0.885229955}
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