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Simplifying 3y2 + 18y + -12 = 0 Reorder the terms: -12 + 18y + 3y2 = 0 Solving -12 + 18y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 6y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 6y + y2)' equal to zero and attempt to solve: Simplifying -4 + 6y + y2 = 0 Solving -4 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 6y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 6y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 6y + y2 = 0 + 4 6y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 6y + y2 = 4 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 = 4 + 9 Reorder the terms: 9 + 6y + y2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + 6y + y2 = 13 Factor a perfect square on the left side: (y + 3)(y + 3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + 3) equal to 3.605551275 and -3.605551275.Subproblem 1
y + 3 = 3.605551275 Simplifying y + 3 = 3.605551275 Reorder the terms: 3 + y = 3.605551275 Solving 3 + y = 3.605551275 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 = 3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.605551275 + -3 y = 3.605551275 + -3 Combine like terms: 3.605551275 + -3 = 0.605551275 y = 0.605551275 Simplifying y = 0.605551275Subproblem 2
y + 3 = -3.605551275 Simplifying y + 3 = -3.605551275 Reorder the terms: 3 + y = -3.605551275 Solving 3 + y = -3.605551275 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 = -3.605551275 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.605551275 + -3 y = -3.605551275 + -3 Combine like terms: -3.605551275 + -3 = -6.605551275 y = -6.605551275 Simplifying y = -6.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.605551275, -6.605551275}Solution
y = {0.605551275, -6.605551275}
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