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Simplifying 4y2 + -16 + 4y2 + -16y + -4 = 0 Reorder the terms: -16 + -4 + -16y + 4y2 + 4y2 = 0 Combine like terms: -16 + -4 = -20 -20 + -16y + 4y2 + 4y2 = 0 Combine like terms: 4y2 + 4y2 = 8y2 -20 + -16y + 8y2 = 0 Solving -20 + -16y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -4y + 2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -4y + 2y2)' equal to zero and attempt to solve: Simplifying -5 + -4y + 2y2 = 0 Solving -5 + -4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -2y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2y + y2 = 0 + 2.5 -2y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2y + y2 = 2.5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 2.5 + 1 Reorder the terms: 1 + -2y + y2 = 2.5 + 1 Combine like terms: 2.5 + 1 = 3.5 1 + -2y + y2 = 3.5 Factor a perfect square on the left side: (y + -1)(y + -1) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (y + -1) equal to 1.870828693 and -1.870828693.Subproblem 1
y + -1 = 1.870828693 Simplifying y + -1 = 1.870828693 Reorder the terms: -1 + y = 1.870828693 Solving -1 + y = 1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.870828693 + 1 y = 1.870828693 + 1 Combine like terms: 1.870828693 + 1 = 2.870828693 y = 2.870828693 Simplifying y = 2.870828693Subproblem 2
y + -1 = -1.870828693 Simplifying y + -1 = -1.870828693 Reorder the terms: -1 + y = -1.870828693 Solving -1 + y = -1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.870828693 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.870828693 + 1 y = -1.870828693 + 1 Combine like terms: -1.870828693 + 1 = -0.870828693 y = -0.870828693 Simplifying y = -0.870828693Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.870828693, -0.870828693}Solution
y = {2.870828693, -0.870828693}
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