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Simplifying 5y2 + 8y + 2 = 0 Reorder the terms: 2 + 8y + 5y2 = 0 Solving 2 + 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'. 0.4 + 1.6y + y2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.6y + -0.4 + y2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.6y + y2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.6y + y2 = 0 + -0.4 1.6y + y2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.6y + y2 = -0.4 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 = -0.4 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = -0.4 + 0.64 Combine like terms: -0.4 + 0.64 = 0.24 0.64 + 1.6y + y2 = 0.24 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (y + 0.8) equal to 0.489897949 and -0.489897949.Subproblem 1
y + 0.8 = 0.489897949 Simplifying y + 0.8 = 0.489897949 Reorder the terms: 0.8 + y = 0.489897949 Solving 0.8 + y = 0.489897949 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 = 0.489897949 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = 0.489897949 + -0.8 y = 0.489897949 + -0.8 Combine like terms: 0.489897949 + -0.8 = -0.310102051 y = -0.310102051 Simplifying y = -0.310102051Subproblem 2
y + 0.8 = -0.489897949 Simplifying y + 0.8 = -0.489897949 Reorder the terms: 0.8 + y = -0.489897949 Solving 0.8 + y = -0.489897949 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 = -0.489897949 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = -0.489897949 + -0.8 y = -0.489897949 + -0.8 Combine like terms: -0.489897949 + -0.8 = -1.289897949 y = -1.289897949 Simplifying y = -1.289897949Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.310102051, -1.289897949}
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