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Simplifying 0.5y2 + 3y + 1 = 0 Reorder the terms: 1 + 3y + 0.5y2 = 0 Solving 1 + 3y + 0.5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 2 + 6y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + 6y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6y + y2 = 0 + -2 6y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 6y + y2 = -2 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -2 + 9 Reorder the terms: 9 + 6y + y2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + 6y + y2 = 7 Factor a perfect square on the left side: (y + 3)(y + 3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + 3) equal to 2.645751311 and -2.645751311.Subproblem 1
y + 3 = 2.645751311 Simplifying y + 3 = 2.645751311 Reorder the terms: 3 + y = 2.645751311 Solving 3 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.645751311 + -3 y = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 y = -0.354248689 Simplifying y = -0.354248689Subproblem 2
y + 3 = -2.645751311 Simplifying y + 3 = -2.645751311 Reorder the terms: 3 + y = -2.645751311 Solving 3 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.645751311 + -3 y = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 y = -5.645751311 Simplifying y = -5.645751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.354248689, -5.645751311}
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