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Simplifying 15y2 + 45y + -12 = 0 Reorder the terms: -12 + 45y + 15y2 = 0 Solving -12 + 45y + 15y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 15y + 5y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 15y + 5y2)' equal to zero and attempt to solve: Simplifying -4 + 15y + 5y2 = 0 Solving -4 + 15y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 3y + y2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 3y + 0.8 + y2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 3y + y2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 3y + y2 = 0 + 0.8 3y + y2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 3y + y2 = 0.8 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 = 0.8 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 0.8 + 2.25 Combine like terms: 0.8 + 2.25 = 3.05 2.25 + 3y + y2 = 3.05 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 3.05 Calculate the square root of the right side: 1.74642492 Break this problem into two subproblems by setting (y + 1.5) equal to 1.74642492 and -1.74642492.Subproblem 1
y + 1.5 = 1.74642492 Simplifying y + 1.5 = 1.74642492 Reorder the terms: 1.5 + y = 1.74642492 Solving 1.5 + y = 1.74642492 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 = 1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 1.74642492 + -1.5 y = 1.74642492 + -1.5 Combine like terms: 1.74642492 + -1.5 = 0.24642492 y = 0.24642492 Simplifying y = 0.24642492Subproblem 2
y + 1.5 = -1.74642492 Simplifying y + 1.5 = -1.74642492 Reorder the terms: 1.5 + y = -1.74642492 Solving 1.5 + y = -1.74642492 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 = -1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -1.74642492 + -1.5 y = -1.74642492 + -1.5 Combine like terms: -1.74642492 + -1.5 = -3.24642492 y = -3.24642492 Simplifying y = -3.24642492Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.24642492, -3.24642492}Solution
y = {0.24642492, -3.24642492}
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