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Simplifying 5y2 + 8y = -1 Reorder the terms: 8y + 5y2 = -1 Solving 8y + 5y2 = -1 Solving for variable 'y'. Reorder the terms: 1 + 8y + 5y2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 8y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 1.6y + y2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 1.6y + -0.2 + y2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 1.6y + y2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 1.6y + y2 = 0 + -0.2 1.6y + y2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 1.6y + y2 = -0.2 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 = -0.2 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = -0.2 + 0.64 Combine like terms: -0.2 + 0.64 = 0.44 0.64 + 1.6y + y2 = 0.44 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = 0.44 Calculate the square root of the right side: 0.663324958 Break this problem into two subproblems by setting (y + 0.8) equal to 0.663324958 and -0.663324958.Subproblem 1
y + 0.8 = 0.663324958 Simplifying y + 0.8 = 0.663324958 Reorder the terms: 0.8 + y = 0.663324958 Solving 0.8 + y = 0.663324958 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 = 0.663324958 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = 0.663324958 + -0.8 y = 0.663324958 + -0.8 Combine like terms: 0.663324958 + -0.8 = -0.136675042 y = -0.136675042 Simplifying y = -0.136675042Subproblem 2
y + 0.8 = -0.663324958 Simplifying y + 0.8 = -0.663324958 Reorder the terms: 0.8 + y = -0.663324958 Solving 0.8 + y = -0.663324958 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 = -0.663324958 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = -0.663324958 + -0.8 y = -0.663324958 + -0.8 Combine like terms: -0.663324958 + -0.8 = -1.463324958 y = -1.463324958 Simplifying y = -1.463324958Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.136675042, -1.463324958}
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