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Simplifying 9 + -6y + 3y2 = 45 Solving 9 + -6y + 3y2 = 45 Solving for variable 'y'. Reorder the terms: 9 + -45 + -6y + 3y2 = 45 + -45 Combine like terms: 9 + -45 = -36 -36 + -6y + 3y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -36 + -6y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -2y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + -2y + y2)' equal to zero and attempt to solve: Simplifying -12 + -2y + y2 = 0 Solving -12 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + -2y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -2y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2y + y2 = 0 + 12 -2y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2y + y2 = 12 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 12 + 1 Reorder the terms: 1 + -2y + y2 = 12 + 1 Combine like terms: 12 + 1 = 13 1 + -2y + y2 = 13 Factor a perfect square on the left side: (y + -1)(y + -1) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + -1) equal to 3.605551275 and -3.605551275.Subproblem 1
y + -1 = 3.605551275 Simplifying y + -1 = 3.605551275 Reorder the terms: -1 + y = 3.605551275 Solving -1 + y = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + y = 3.605551275 + 1 y = 3.605551275 + 1 Combine like terms: 3.605551275 + 1 = 4.605551275 y = 4.605551275 Simplifying y = 4.605551275Subproblem 2
y + -1 = -3.605551275 Simplifying y + -1 = -3.605551275 Reorder the terms: -1 + y = -3.605551275 Solving -1 + y = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -3.605551275 + 1 Combine like terms: -1 + 1 = 0 0 + y = -3.605551275 + 1 y = -3.605551275 + 1 Combine like terms: -3.605551275 + 1 = -2.605551275 y = -2.605551275 Simplifying y = -2.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.605551275, -2.605551275}Solution
y = {4.605551275, -2.605551275}
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