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Simplifying (9(174 + -1y)) * 6y = 1244 ((174 * 9 + -1y * 9)) * 6y = 1244 ((1566 + -9y)) * 6y = 1244 Reorder the terms for easier multiplication: 6y(1566 + -9y) = 1244 (1566 * 6y + -9y * 6y) = 1244 (9396y + -54y2) = 1244 Solving 9396y + -54y2 = 1244 Solving for variable 'y'. Reorder the terms: -1244 + 9396y + -54y2 = 1244 + -1244 Combine like terms: 1244 + -1244 = 0 -1244 + 9396y + -54y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-622 + 4698y + -27y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-622 + 4698y + -27y2)' equal to zero and attempt to solve: Simplifying -622 + 4698y + -27y2 = 0 Solving -622 + 4698y + -27y2 = 0 Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. 23.03703704 + -174y + y2 = 0 Move the constant term to the right: Add '-23.03703704' to each side of the equation. 23.03703704 + -174y + -23.03703704 + y2 = 0 + -23.03703704 Reorder the terms: 23.03703704 + -23.03703704 + -174y + y2 = 0 + -23.03703704 Combine like terms: 23.03703704 + -23.03703704 = 0.00000000 0.00000000 + -174y + y2 = 0 + -23.03703704 -174y + y2 = 0 + -23.03703704 Combine like terms: 0 + -23.03703704 = -23.03703704 -174y + y2 = -23.03703704 The y term is -174y. Take half its coefficient (-87). Square it (7569) and add it to both sides. Add '7569' to each side of the equation. -174y + 7569 + y2 = -23.03703704 + 7569 Reorder the terms: 7569 + -174y + y2 = -23.03703704 + 7569 Combine like terms: -23.03703704 + 7569 = 7545.96296296 7569 + -174y + y2 = 7545.96296296 Factor a perfect square on the left side: (y + -87)(y + -87) = 7545.96296296 Calculate the square root of the right side: 86.867502341 Break this problem into two subproblems by setting (y + -87) equal to 86.867502341 and -86.867502341.Subproblem 1
y + -87 = 86.867502341 Simplifying y + -87 = 86.867502341 Reorder the terms: -87 + y = 86.867502341 Solving -87 + y = 86.867502341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '87' to each side of the equation. -87 + 87 + y = 86.867502341 + 87 Combine like terms: -87 + 87 = 0 0 + y = 86.867502341 + 87 y = 86.867502341 + 87 Combine like terms: 86.867502341 + 87 = 173.867502341 y = 173.867502341 Simplifying y = 173.867502341Subproblem 2
y + -87 = -86.867502341 Simplifying y + -87 = -86.867502341 Reorder the terms: -87 + y = -86.867502341 Solving -87 + y = -86.867502341 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '87' to each side of the equation. -87 + 87 + y = -86.867502341 + 87 Combine like terms: -87 + 87 = 0 0 + y = -86.867502341 + 87 y = -86.867502341 + 87 Combine like terms: -86.867502341 + 87 = 0.132497659 y = 0.132497659 Simplifying y = 0.132497659Solution
The solution to the problem is based on the solutions from the subproblems. y = {173.867502341, 0.132497659}Solution
y = {173.867502341, 0.132497659}
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