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Simplifying -4y(y + 6) = 24 Reorder the terms: -4y(6 + y) = 24 (6 * -4y + y * -4y) = 24 (-24y + -4y2) = 24 Solving -24y + -4y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + -24y + -4y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -24y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(6 + 6y + y2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(6 + 6y + y2)' equal to zero and attempt to solve: Simplifying 6 + 6y + y2 = 0 Solving 6 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 6y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + 6y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 6y + y2 = 0 + -6 6y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 6y + y2 = -6 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 = -6 + 9 Reorder the terms: 9 + 6y + y2 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + 6y + y2 = 3 Factor a perfect square on the left side: (y + 3)(y + 3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + 3) equal to 1.732050808 and -1.732050808.Subproblem 1
y + 3 = 1.732050808 Simplifying y + 3 = 1.732050808 Reorder the terms: 3 + y = 1.732050808 Solving 3 + y = 1.732050808 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 = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + y = 1.732050808 + -3 y = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 y = -1.267949192 Simplifying y = -1.267949192Subproblem 2
y + 3 = -1.732050808 Simplifying y + 3 = -1.732050808 Reorder the terms: 3 + y = -1.732050808 Solving 3 + y = -1.732050808 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 = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + y = -1.732050808 + -3 y = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 y = -4.732050808 Simplifying y = -4.732050808Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.267949192, -4.732050808}Solution
y = {-1.267949192, -4.732050808}
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