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Simplifying 4y2 + -34y + -32 = 0 Reorder the terms: -32 + -34y + 4y2 = 0 Solving -32 + -34y + 4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -17y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -17y + 2y2)' equal to zero and attempt to solve: Simplifying -16 + -17y + 2y2 = 0 Solving -16 + -17y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8 + -8.5y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -8.5y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -8.5y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -8.5y + y2 = 0 + 8 -8.5y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -8.5y + y2 = 8 The y term is -8.5y. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5y + 18.0625 + y2 = 8 + 18.0625 Reorder the terms: 18.0625 + -8.5y + y2 = 8 + 18.0625 Combine like terms: 8 + 18.0625 = 26.0625 18.0625 + -8.5y + y2 = 26.0625 Factor a perfect square on the left side: (y + -4.25)(y + -4.25) = 26.0625 Calculate the square root of the right side: 5.105144464 Break this problem into two subproblems by setting (y + -4.25) equal to 5.105144464 and -5.105144464.Subproblem 1
y + -4.25 = 5.105144464 Simplifying y + -4.25 = 5.105144464 Reorder the terms: -4.25 + y = 5.105144464 Solving -4.25 + y = 5.105144464 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = 5.105144464 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = 5.105144464 + 4.25 y = 5.105144464 + 4.25 Combine like terms: 5.105144464 + 4.25 = 9.355144464 y = 9.355144464 Simplifying y = 9.355144464Subproblem 2
y + -4.25 = -5.105144464 Simplifying y + -4.25 = -5.105144464 Reorder the terms: -4.25 + y = -5.105144464 Solving -4.25 + y = -5.105144464 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = -5.105144464 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = -5.105144464 + 4.25 y = -5.105144464 + 4.25 Combine like terms: -5.105144464 + 4.25 = -0.855144464 y = -0.855144464 Simplifying y = -0.855144464Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.355144464, -0.855144464}Solution
y = {9.355144464, -0.855144464}
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