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Simplifying 3y2 + 15y = 12 Reorder the terms: 15y + 3y2 = 12 Solving 15y + 3y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + 15y + 3y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 15y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5y + y2)' equal to zero and attempt to solve: Simplifying -4 + 5y + y2 = 0 Solving -4 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 5y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 5y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5y + y2 = 0 + 4 5y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 5y + y2 = 4 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = 4 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + 5y + y2 = 10.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + 2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
y + 2.5 = 3.201562119 Simplifying y + 2.5 = 3.201562119 Reorder the terms: 2.5 + y = 3.201562119 Solving 2.5 + y = 3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 3.201562119 + -2.5 y = 3.201562119 + -2.5 Combine like terms: 3.201562119 + -2.5 = 0.701562119 y = 0.701562119 Simplifying y = 0.701562119Subproblem 2
y + 2.5 = -3.201562119 Simplifying y + 2.5 = -3.201562119 Reorder the terms: 2.5 + y = -3.201562119 Solving 2.5 + y = -3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -3.201562119 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -3.201562119 + -2.5 y = -3.201562119 + -2.5 Combine like terms: -3.201562119 + -2.5 = -5.701562119 y = -5.701562119 Simplifying y = -5.701562119Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.701562119, -5.701562119}Solution
y = {0.701562119, -5.701562119}
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