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Simplifying 6y2 + -4y + 3 + -5y2 + -4y + 6 = 0 Reorder the terms: 3 + 6 + -4y + -4y + 6y2 + -5y2 = 0 Combine like terms: 3 + 6 = 9 9 + -4y + -4y + 6y2 + -5y2 = 0 Combine like terms: -4y + -4y = -8y 9 + -8y + 6y2 + -5y2 = 0 Combine like terms: 6y2 + -5y2 = 1y2 9 + -8y + 1y2 = 0 Solving 9 + -8y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + -8y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8y + y2 = 0 + -9 -8y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8y + y2 = -9 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -9 + 16 Reorder the terms: 16 + -8y + y2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8y + y2 = 7 Factor a perfect square on the left side: (y + -4)(y + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -4 = 2.645751311 Simplifying y + -4 = 2.645751311 Reorder the terms: -4 + y = 2.645751311 Solving -4 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + y = 2.645751311 + 4 y = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 y = 6.645751311 Simplifying y = 6.645751311Subproblem 2
y + -4 = -2.645751311 Simplifying y + -4 = -2.645751311 Reorder the terms: -4 + y = -2.645751311 Solving -4 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + y = -2.645751311 + 4 y = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 y = 1.354248689 Simplifying y = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.645751311, 1.354248689}
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