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Simplifying 8y2 + -26y + -336 = 0 Reorder the terms: -336 + -26y + 8y2 = 0 Solving -336 + -26y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-168 + -13y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-168 + -13y + 4y2)' equal to zero and attempt to solve: Simplifying -168 + -13y + 4y2 = 0 Solving -168 + -13y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -42 + -3.25y + y2 = 0 Move the constant term to the right: Add '42' to each side of the equation. -42 + -3.25y + 42 + y2 = 0 + 42 Reorder the terms: -42 + 42 + -3.25y + y2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -3.25y + y2 = 0 + 42 -3.25y + y2 = 0 + 42 Combine like terms: 0 + 42 = 42 -3.25y + y2 = 42 The y term is -3.25y. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25y + 2.640625 + y2 = 42 + 2.640625 Reorder the terms: 2.640625 + -3.25y + y2 = 42 + 2.640625 Combine like terms: 42 + 2.640625 = 44.640625 2.640625 + -3.25y + y2 = 44.640625 Factor a perfect square on the left side: (y + -1.625)(y + -1.625) = 44.640625 Calculate the square root of the right side: 6.681364007 Break this problem into two subproblems by setting (y + -1.625) equal to 6.681364007 and -6.681364007.Subproblem 1
y + -1.625 = 6.681364007 Simplifying y + -1.625 = 6.681364007 Reorder the terms: -1.625 + y = 6.681364007 Solving -1.625 + y = 6.681364007 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = 6.681364007 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = 6.681364007 + 1.625 y = 6.681364007 + 1.625 Combine like terms: 6.681364007 + 1.625 = 8.306364007 y = 8.306364007 Simplifying y = 8.306364007Subproblem 2
y + -1.625 = -6.681364007 Simplifying y + -1.625 = -6.681364007 Reorder the terms: -1.625 + y = -6.681364007 Solving -1.625 + y = -6.681364007 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = -6.681364007 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = -6.681364007 + 1.625 y = -6.681364007 + 1.625 Combine like terms: -6.681364007 + 1.625 = -5.056364007 y = -5.056364007 Simplifying y = -5.056364007Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.306364007, -5.056364007}Solution
y = {8.306364007, -5.056364007}
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