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Simplifying 2y2 + -24y + 18 = 0 Reorder the terms: 18 + -24y + 2y2 = 0 Solving 18 + -24y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -12y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -12y + y2)' equal to zero and attempt to solve: Simplifying 9 + -12y + y2 = 0 Solving 9 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -12y + -9 + y2 = 0 + -9 Reorder the terms: 9 + -9 + -12y + y2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -12y + y2 = 0 + -9 -12y + y2 = 0 + -9 Combine like terms: 0 + -9 = -9 -12y + y2 = -9 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -9 + 36 Reorder the terms: 36 + -12y + y2 = -9 + 36 Combine like terms: -9 + 36 = 27 36 + -12y + y2 = 27 Factor a perfect square on the left side: (y + -6)(y + -6) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -6) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -6 = 5.196152423 Simplifying y + -6 = 5.196152423 Reorder the terms: -6 + y = 5.196152423 Solving -6 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y = 5.196152423 + 6 y = 5.196152423 + 6 Combine like terms: 5.196152423 + 6 = 11.196152423 y = 11.196152423 Simplifying y = 11.196152423Subproblem 2
y + -6 = -5.196152423 Simplifying y + -6 = -5.196152423 Reorder the terms: -6 + y = -5.196152423 Solving -6 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -5.196152423 + 6 Combine like terms: -6 + 6 = 0 0 + y = -5.196152423 + 6 y = -5.196152423 + 6 Combine like terms: -5.196152423 + 6 = 0.803847577 y = 0.803847577 Simplifying y = 0.803847577Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.196152423, 0.803847577}Solution
y = {11.196152423, 0.803847577}
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