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Simplifying 16y2 + -32y + -44 = 0 Reorder the terms: -44 + -32y + 16y2 = 0 Solving -44 + -32y + 16y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11 + -8y + 4y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-11 + -8y + 4y2)' equal to zero and attempt to solve: Simplifying -11 + -8y + 4y2 = 0 Solving -11 + -8y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -2y + y2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -2y + 2.75 + y2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -2y + y2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -2y + y2 = 0 + 2.75 -2y + y2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -2y + y2 = 2.75 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 = 2.75 + 1 Reorder the terms: 1 + -2y + y2 = 2.75 + 1 Combine like terms: 2.75 + 1 = 3.75 1 + -2y + y2 = 3.75 Factor a perfect square on the left side: (y + -1)(y + -1) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (y + -1) equal to 1.936491673 and -1.936491673.Subproblem 1
y + -1 = 1.936491673 Simplifying y + -1 = 1.936491673 Reorder the terms: -1 + y = 1.936491673 Solving -1 + y = 1.936491673 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 = 1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.936491673 + 1 y = 1.936491673 + 1 Combine like terms: 1.936491673 + 1 = 2.936491673 y = 2.936491673 Simplifying y = 2.936491673Subproblem 2
y + -1 = -1.936491673 Simplifying y + -1 = -1.936491673 Reorder the terms: -1 + y = -1.936491673 Solving -1 + y = -1.936491673 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 = -1.936491673 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.936491673 + 1 y = -1.936491673 + 1 Combine like terms: -1.936491673 + 1 = -0.936491673 y = -0.936491673 Simplifying y = -0.936491673Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.936491673, -0.936491673}Solution
y = {2.936491673, -0.936491673}
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