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Simplifying 6y2 + 6y = 94 Reorder the terms: 6y + 6y2 = 94 Solving 6y + 6y2 = 94 Solving for variable 'y'. Reorder the terms: -94 + 6y + 6y2 = 94 + -94 Combine like terms: 94 + -94 = 0 -94 + 6y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-47 + 3y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-47 + 3y + 3y2)' equal to zero and attempt to solve: Simplifying -47 + 3y + 3y2 = 0 Solving -47 + 3y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15.66666667 + y + y2 = 0 Move the constant term to the right: Add '15.66666667' to each side of the equation. -15.66666667 + y + 15.66666667 + y2 = 0 + 15.66666667 Reorder the terms: -15.66666667 + 15.66666667 + y + y2 = 0 + 15.66666667 Combine like terms: -15.66666667 + 15.66666667 = 0.00000000 0.00000000 + y + y2 = 0 + 15.66666667 y + y2 = 0 + 15.66666667 Combine like terms: 0 + 15.66666667 = 15.66666667 y + y2 = 15.66666667 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + y2 = 15.66666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = 15.66666667 + 0.25 Combine like terms: 15.66666667 + 0.25 = 15.91666667 1.25 + y2 = 15.91666667 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 15.91666667 Calculate the square root of the right side: 3.989569735 Break this problem into two subproblems by setting (y + 0.5) equal to 3.989569735 and -3.989569735.Subproblem 1
y + 0.5 = 3.989569735 Simplifying y + 0.5 = 3.989569735 Reorder the terms: 0.5 + y = 3.989569735 Solving 0.5 + y = 3.989569735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.989569735 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.989569735 + -0.5 y = 3.989569735 + -0.5 Combine like terms: 3.989569735 + -0.5 = 3.489569735 y = 3.489569735 Simplifying y = 3.489569735Subproblem 2
y + 0.5 = -3.989569735 Simplifying y + 0.5 = -3.989569735 Reorder the terms: 0.5 + y = -3.989569735 Solving 0.5 + y = -3.989569735 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.989569735 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.989569735 + -0.5 y = -3.989569735 + -0.5 Combine like terms: -3.989569735 + -0.5 = -4.489569735 y = -4.489569735 Simplifying y = -4.489569735Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.489569735, -4.489569735}Solution
y = {3.489569735, -4.489569735}
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