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Simplifying 8y2 + 42y + -16 = 0 Reorder the terms: -16 + 42y + 8y2 = 0 Solving -16 + 42y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 21y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 21y + 4y2)' equal to zero and attempt to solve: Simplifying -8 + 21y + 4y2 = 0 Solving -8 + 21y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 5.25y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 5.25y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 5.25y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5.25y + y2 = 0 + 2 5.25y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 5.25y + y2 = 2 The y term is 5.25y. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25y + 6.890625 + y2 = 2 + 6.890625 Reorder the terms: 6.890625 + 5.25y + y2 = 2 + 6.890625 Combine like terms: 2 + 6.890625 = 8.890625 6.890625 + 5.25y + y2 = 8.890625 Factor a perfect square on the left side: (y + 2.625)(y + 2.625) = 8.890625 Calculate the square root of the right side: 2.98171511 Break this problem into two subproblems by setting (y + 2.625) equal to 2.98171511 and -2.98171511.Subproblem 1
y + 2.625 = 2.98171511 Simplifying y + 2.625 = 2.98171511 Reorder the terms: 2.625 + y = 2.98171511 Solving 2.625 + y = 2.98171511 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + y = 2.98171511 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + y = 2.98171511 + -2.625 y = 2.98171511 + -2.625 Combine like terms: 2.98171511 + -2.625 = 0.35671511 y = 0.35671511 Simplifying y = 0.35671511Subproblem 2
y + 2.625 = -2.98171511 Simplifying y + 2.625 = -2.98171511 Reorder the terms: 2.625 + y = -2.98171511 Solving 2.625 + y = -2.98171511 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + y = -2.98171511 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + y = -2.98171511 + -2.625 y = -2.98171511 + -2.625 Combine like terms: -2.98171511 + -2.625 = -5.60671511 y = -5.60671511 Simplifying y = -5.60671511Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.35671511, -5.60671511}Solution
y = {0.35671511, -5.60671511}
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