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Simplifying 4y2 + 24y = 6 Reorder the terms: 24y + 4y2 = 6 Solving 24y + 4y2 = 6 Solving for variable 'y'. Reorder the terms: -6 + 24y + 4y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 24y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 12y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 12y + 2y2)' equal to zero and attempt to solve: Simplifying -3 + 12y + 2y2 = 0 Solving -3 + 12y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 6y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 6y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 6y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 6y + y2 = 0 + 1.5 6y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 6y + y2 = 1.5 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 1.5 + 9 Reorder the terms: 9 + 6y + y2 = 1.5 + 9 Combine like terms: 1.5 + 9 = 10.5 9 + 6y + y2 = 10.5 Factor a perfect square on the left side: (y + 3)(y + 3) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (y + 3) equal to 3.240370349 and -3.240370349.Subproblem 1
y + 3 = 3.240370349 Simplifying y + 3 = 3.240370349 Reorder the terms: 3 + y = 3.240370349 Solving 3 + y = 3.240370349 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 3.240370349 + -3 Combine like terms: 3 + -3 = 0 0 + y = 3.240370349 + -3 y = 3.240370349 + -3 Combine like terms: 3.240370349 + -3 = 0.240370349 y = 0.240370349 Simplifying y = 0.240370349Subproblem 2
y + 3 = -3.240370349 Simplifying y + 3 = -3.240370349 Reorder the terms: 3 + y = -3.240370349 Solving 3 + y = -3.240370349 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -3.240370349 + -3 Combine like terms: 3 + -3 = 0 0 + y = -3.240370349 + -3 y = -3.240370349 + -3 Combine like terms: -3.240370349 + -3 = -6.240370349 y = -6.240370349 Simplifying y = -6.240370349Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.240370349, -6.240370349}Solution
y = {0.240370349, -6.240370349}
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