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Simplifying 4y2 + 24y + 16 = 0 Reorder the terms: 16 + 24y + 4y2 = 0 Solving 16 + 24y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 6y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + 6y + y2)' equal to zero and attempt to solve: Simplifying 4 + 6y + y2 = 0 Solving 4 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 6y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + 6y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6y + y2 = 0 + -4 6y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 6y + y2 = -4 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 = -4 + 9 Reorder the terms: 9 + 6y + y2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + 6y + y2 = 5 Factor a perfect square on the left side: (y + 3)(y + 3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + 3) equal to 2.236067978 and -2.236067978.Subproblem 1
y + 3 = 2.236067978 Simplifying y + 3 = 2.236067978 Reorder the terms: 3 + y = 2.236067978 Solving 3 + y = 2.236067978 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 = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.236067978 + -3 y = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 y = -0.763932022 Simplifying y = -0.763932022Subproblem 2
y + 3 = -2.236067978 Simplifying y + 3 = -2.236067978 Reorder the terms: 3 + y = -2.236067978 Solving 3 + y = -2.236067978 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 = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.236067978 + -3 y = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 y = -5.236067978 Simplifying y = -5.236067978Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.763932022, -5.236067978}Solution
y = {-0.763932022, -5.236067978}
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