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Simplifying 5y2 + 11y + 4 = 0 Reorder the terms: 4 + 11y + 5y2 = 0 Solving 4 + 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'. 0.8 + 2.2y + y2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 2.2y + -0.8 + y2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 2.2y + y2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 2.2y + y2 = 0 + -0.8 2.2y + y2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 2.2y + y2 = -0.8 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 = -0.8 + 1.21 Reorder the terms: 1.21 + 2.2y + y2 = -0.8 + 1.21 Combine like terms: -0.8 + 1.21 = 0.41 1.21 + 2.2y + y2 = 0.41 Factor a perfect square on the left side: (y + 1.1)(y + 1.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (y + 1.1) equal to 0.640312424 and -0.640312424.Subproblem 1
y + 1.1 = 0.640312424 Simplifying y + 1.1 = 0.640312424 Reorder the terms: 1.1 + y = 0.640312424 Solving 1.1 + y = 0.640312424 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 = 0.640312424 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + y = 0.640312424 + -1.1 y = 0.640312424 + -1.1 Combine like terms: 0.640312424 + -1.1 = -0.459687576 y = -0.459687576 Simplifying y = -0.459687576Subproblem 2
y + 1.1 = -0.640312424 Simplifying y + 1.1 = -0.640312424 Reorder the terms: 1.1 + y = -0.640312424 Solving 1.1 + y = -0.640312424 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 = -0.640312424 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + y = -0.640312424 + -1.1 y = -0.640312424 + -1.1 Combine like terms: -0.640312424 + -1.1 = -1.740312424 y = -1.740312424 Simplifying y = -1.740312424Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.459687576, -1.740312424}
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