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Simplifying 3y2 + 45y + -3600 = 0 Reorder the terms: -3600 + 45y + 3y2 = 0 Solving -3600 + 45y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1200 + 15y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1200 + 15y + y2)' equal to zero and attempt to solve: Simplifying -1200 + 15y + y2 = 0 Solving -1200 + 15y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 15y + 1200 + y2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 15y + y2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 15y + y2 = 0 + 1200 15y + y2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 15y + y2 = 1200 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = 1200 + 56.25 Reorder the terms: 56.25 + 15y + y2 = 1200 + 56.25 Combine like terms: 1200 + 56.25 = 1256.25 56.25 + 15y + y2 = 1256.25 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = 1256.25 Calculate the square root of the right side: 35.443617197 Break this problem into two subproblems by setting (y + 7.5) equal to 35.443617197 and -35.443617197.Subproblem 1
y + 7.5 = 35.443617197 Simplifying y + 7.5 = 35.443617197 Reorder the terms: 7.5 + y = 35.443617197 Solving 7.5 + y = 35.443617197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = 35.443617197 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = 35.443617197 + -7.5 y = 35.443617197 + -7.5 Combine like terms: 35.443617197 + -7.5 = 27.943617197 y = 27.943617197 Simplifying y = 27.943617197Subproblem 2
y + 7.5 = -35.443617197 Simplifying y + 7.5 = -35.443617197 Reorder the terms: 7.5 + y = -35.443617197 Solving 7.5 + y = -35.443617197 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = -35.443617197 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = -35.443617197 + -7.5 y = -35.443617197 + -7.5 Combine like terms: -35.443617197 + -7.5 = -42.943617197 y = -42.943617197 Simplifying y = -42.943617197Solution
The solution to the problem is based on the solutions from the subproblems. y = {27.943617197, -42.943617197}Solution
y = {27.943617197, -42.943617197}
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