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Simplifying -4y2 + -112y = -44 Reorder the terms: -112y + -4y2 = -44 Solving -112y + -4y2 = -44 Solving for variable 'y'. Reorder the terms: 44 + -112y + -4y2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + -112y + -4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(11 + -28y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -28y + -1y2)' equal to zero and attempt to solve: Simplifying 11 + -28y + -1y2 = 0 Solving 11 + -28y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + 28y + y2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + 28y + 11 + y2 = 0 + 11 Reorder the terms: -11 + 11 + 28y + y2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 28y + y2 = 0 + 11 28y + y2 = 0 + 11 Combine like terms: 0 + 11 = 11 28y + y2 = 11 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = 11 + 196 Reorder the terms: 196 + 28y + y2 = 11 + 196 Combine like terms: 11 + 196 = 207 196 + 28y + y2 = 207 Factor a perfect square on the left side: (y + 14)(y + 14) = 207 Calculate the square root of the right side: 14.38749457 Break this problem into two subproblems by setting (y + 14) equal to 14.38749457 and -14.38749457.Subproblem 1
y + 14 = 14.38749457 Simplifying y + 14 = 14.38749457 Reorder the terms: 14 + y = 14.38749457 Solving 14 + y = 14.38749457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + y = 14.38749457 + -14 y = 14.38749457 + -14 Combine like terms: 14.38749457 + -14 = 0.38749457 y = 0.38749457 Simplifying y = 0.38749457Subproblem 2
y + 14 = -14.38749457 Simplifying y + 14 = -14.38749457 Reorder the terms: 14 + y = -14.38749457 Solving 14 + y = -14.38749457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -14.38749457 + -14 Combine like terms: 14 + -14 = 0 0 + y = -14.38749457 + -14 y = -14.38749457 + -14 Combine like terms: -14.38749457 + -14 = -28.38749457 y = -28.38749457 Simplifying y = -28.38749457Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.38749457, -28.38749457}Solution
y = {0.38749457, -28.38749457}
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