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Simplifying 2y2 + 12y + -7 = 0 Reorder the terms: -7 + 12y + 2y2 = 0 Solving -7 + 12y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 6y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 6y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 6y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 6y + y2 = 0 + 3.5 6y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 6y + y2 = 3.5 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 = 3.5 + 9 Reorder the terms: 9 + 6y + y2 = 3.5 + 9 Combine like terms: 3.5 + 9 = 12.5 9 + 6y + y2 = 12.5 Factor a perfect square on the left side: (y + 3)(y + 3) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (y + 3) equal to 3.535533906 and -3.535533906.Subproblem 1
y + 3 = 3.535533906 Simplifying y + 3 = 3.535533906 Reorder the terms: 3 + y = 3.535533906 Solving 3 + y = 3.535533906 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 = 3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.535533906 + -3 y = 3.535533906 + -3 Combine like terms: 3.535533906 + -3 = 0.535533906 y = 0.535533906 Simplifying y = 0.535533906Subproblem 2
y + 3 = -3.535533906 Simplifying y + 3 = -3.535533906 Reorder the terms: 3 + y = -3.535533906 Solving 3 + y = -3.535533906 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 = -3.535533906 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.535533906 + -3 y = -3.535533906 + -3 Combine like terms: -3.535533906 + -3 = -6.535533906 y = -6.535533906 Simplifying y = -6.535533906Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.535533906, -6.535533906}
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