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Simplifying 3y2 + 12y = 9 Reorder the terms: 12y + 3y2 = 9 Solving 12y + 3y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + 12y + 3y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 12y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 4y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 4y + y2)' equal to zero and attempt to solve: Simplifying -3 + 4y + y2 = 0 Solving -3 + 4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 4y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4y + y2 = 0 + 3 4y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 4y + y2 = 3 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 3 + 4 Reorder the terms: 4 + 4y + y2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4y + y2 = 7 Factor a perfect square on the left side: (y + 2)(y + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
y + 2 = 2.645751311 Simplifying y + 2 = 2.645751311 Reorder the terms: 2 + y = 2.645751311 Solving 2 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + y = 2.645751311 + -2 y = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 y = 0.645751311 Simplifying y = 0.645751311Subproblem 2
y + 2 = -2.645751311 Simplifying y + 2 = -2.645751311 Reorder the terms: 2 + y = -2.645751311 Solving 2 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + y = -2.645751311 + -2 y = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 y = -4.645751311 Simplifying y = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.645751311, -4.645751311}Solution
y = {0.645751311, -4.645751311}
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