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Simplifying 3y2 + 42y = 93 Reorder the terms: 42y + 3y2 = 93 Solving 42y + 3y2 = 93 Solving for variable 'y'. Reorder the terms: -93 + 42y + 3y2 = 93 + -93 Combine like terms: 93 + -93 = 0 -93 + 42y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-31 + 14y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-31 + 14y + y2)' equal to zero and attempt to solve: Simplifying -31 + 14y + y2 = 0 Solving -31 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 14y + 31 + y2 = 0 + 31 Reorder the terms: -31 + 31 + 14y + y2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 14y + y2 = 0 + 31 14y + y2 = 0 + 31 Combine like terms: 0 + 31 = 31 14y + y2 = 31 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = 31 + 49 Reorder the terms: 49 + 14y + y2 = 31 + 49 Combine like terms: 31 + 49 = 80 49 + 14y + y2 = 80 Factor a perfect square on the left side: (y + 7)(y + 7) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (y + 7) equal to 8.94427191 and -8.94427191.Subproblem 1
y + 7 = 8.94427191 Simplifying y + 7 = 8.94427191 Reorder the terms: 7 + y = 8.94427191 Solving 7 + y = 8.94427191 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + y = 8.94427191 + -7 y = 8.94427191 + -7 Combine like terms: 8.94427191 + -7 = 1.94427191 y = 1.94427191 Simplifying y = 1.94427191Subproblem 2
y + 7 = -8.94427191 Simplifying y + 7 = -8.94427191 Reorder the terms: 7 + y = -8.94427191 Solving 7 + y = -8.94427191 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = -8.94427191 + -7 Combine like terms: 7 + -7 = 0 0 + y = -8.94427191 + -7 y = -8.94427191 + -7 Combine like terms: -8.94427191 + -7 = -15.94427191 y = -15.94427191 Simplifying y = -15.94427191Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.94427191, -15.94427191}Solution
y = {1.94427191, -15.94427191}
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