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Simplifying 3y2 + -234y + 945 = 0 Reorder the terms: 945 + -234y + 3y2 = 0 Solving 945 + -234y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(315 + -78y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(315 + -78y + y2)' equal to zero and attempt to solve: Simplifying 315 + -78y + y2 = 0 Solving 315 + -78y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-315' to each side of the equation. 315 + -78y + -315 + y2 = 0 + -315 Reorder the terms: 315 + -315 + -78y + y2 = 0 + -315 Combine like terms: 315 + -315 = 0 0 + -78y + y2 = 0 + -315 -78y + y2 = 0 + -315 Combine like terms: 0 + -315 = -315 -78y + y2 = -315 The y term is -78y. Take half its coefficient (-39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. -78y + 1521 + y2 = -315 + 1521 Reorder the terms: 1521 + -78y + y2 = -315 + 1521 Combine like terms: -315 + 1521 = 1206 1521 + -78y + y2 = 1206 Factor a perfect square on the left side: (y + -39)(y + -39) = 1206 Calculate the square root of the right side: 34.727510708 Break this problem into two subproblems by setting (y + -39) equal to 34.727510708 and -34.727510708.Subproblem 1
y + -39 = 34.727510708 Simplifying y + -39 = 34.727510708 Reorder the terms: -39 + y = 34.727510708 Solving -39 + y = 34.727510708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + y = 34.727510708 + 39 Combine like terms: -39 + 39 = 0 0 + y = 34.727510708 + 39 y = 34.727510708 + 39 Combine like terms: 34.727510708 + 39 = 73.727510708 y = 73.727510708 Simplifying y = 73.727510708Subproblem 2
y + -39 = -34.727510708 Simplifying y + -39 = -34.727510708 Reorder the terms: -39 + y = -34.727510708 Solving -39 + y = -34.727510708 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + y = -34.727510708 + 39 Combine like terms: -39 + 39 = 0 0 + y = -34.727510708 + 39 y = -34.727510708 + 39 Combine like terms: -34.727510708 + 39 = 4.272489292 y = 4.272489292 Simplifying y = 4.272489292Solution
The solution to the problem is based on the solutions from the subproblems. y = {73.727510708, 4.272489292}Solution
y = {73.727510708, 4.272489292}
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