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Simplifying 6y + 12y + 13 = 2y2 + 4 Reorder the terms: 13 + 6y + 12y = 2y2 + 4 Combine like terms: 6y + 12y = 18y 13 + 18y = 2y2 + 4 Reorder the terms: 13 + 18y = 4 + 2y2 Solving 13 + 18y = 4 + 2y2 Solving for variable 'y'. Reorder the terms: 13 + -4 + 18y + -2y2 = 4 + 2y2 + -4 + -2y2 Combine like terms: 13 + -4 = 9 9 + 18y + -2y2 = 4 + 2y2 + -4 + -2y2 Reorder the terms: 9 + 18y + -2y2 = 4 + -4 + 2y2 + -2y2 Combine like terms: 4 + -4 = 0 9 + 18y + -2y2 = 0 + 2y2 + -2y2 9 + 18y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 9 + 18y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -9y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -9y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -9y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -9y + y2 = 0 + 4.5 -9y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -9y + y2 = 4.5 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 4.5 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 4.5 + 20.25 Combine like terms: 4.5 + 20.25 = 24.75 20.25 + -9y + y2 = 24.75 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (y + -4.5) equal to 4.974937186 and -4.974937186.Subproblem 1
y + -4.5 = 4.974937186 Simplifying y + -4.5 = 4.974937186 Reorder the terms: -4.5 + y = 4.974937186 Solving -4.5 + y = 4.974937186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 4.974937186 + 4.5 y = 4.974937186 + 4.5 Combine like terms: 4.974937186 + 4.5 = 9.474937186 y = 9.474937186 Simplifying y = 9.474937186Subproblem 2
y + -4.5 = -4.974937186 Simplifying y + -4.5 = -4.974937186 Reorder the terms: -4.5 + y = -4.974937186 Solving -4.5 + y = -4.974937186 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -4.974937186 + 4.5 y = -4.974937186 + 4.5 Combine like terms: -4.974937186 + 4.5 = -0.474937186 y = -0.474937186 Simplifying y = -0.474937186Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.474937186, -0.474937186}
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