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Simplifying 4y2 + -12y + 9 = 45 Reorder the terms: 9 + -12y + 4y2 = 45 Solving 9 + -12y + 4y2 = 45 Solving for variable 'y'. Reorder the terms: 9 + -45 + -12y + 4y2 = 45 + -45 Combine like terms: 9 + -45 = -36 -36 + -12y + 4y2 = 45 + -45 Combine like terms: 45 + -45 = 0 -36 + -12y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -3y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -3y + y2)' equal to zero and attempt to solve: Simplifying -9 + -3y + y2 = 0 Solving -9 + -3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -3y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -3y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -3y + y2 = 0 + 9 -3y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -3y + y2 = 9 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 9 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 9 + 2.25 Combine like terms: 9 + 2.25 = 11.25 2.25 + -3y + y2 = 11.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (y + -1.5) equal to 3.354101966 and -3.354101966.Subproblem 1
y + -1.5 = 3.354101966 Simplifying y + -1.5 = 3.354101966 Reorder the terms: -1.5 + y = 3.354101966 Solving -1.5 + y = 3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.354101966 + 1.5 y = 3.354101966 + 1.5 Combine like terms: 3.354101966 + 1.5 = 4.854101966 y = 4.854101966 Simplifying y = 4.854101966Subproblem 2
y + -1.5 = -3.354101966 Simplifying y + -1.5 = -3.354101966 Reorder the terms: -1.5 + y = -3.354101966 Solving -1.5 + y = -3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.354101966 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.354101966 + 1.5 y = -3.354101966 + 1.5 Combine like terms: -3.354101966 + 1.5 = -1.854101966 y = -1.854101966 Simplifying y = -1.854101966Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.854101966, -1.854101966}Solution
y = {4.854101966, -1.854101966}
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