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Simplifying y2 + -24y = 35 Reorder the terms: -24y + y2 = 35 Solving -24y + y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + -24y + y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -24y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -24y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + -24y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -24y + y2 = 0 + 35 -24y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -24y + y2 = 35 The y term is -24y. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24y + 144 + y2 = 35 + 144 Reorder the terms: 144 + -24y + y2 = 35 + 144 Combine like terms: 35 + 144 = 179 144 + -24y + y2 = 179 Factor a perfect square on the left side: (y + -12)(y + -12) = 179 Calculate the square root of the right side: 13.37908816 Break this problem into two subproblems by setting (y + -12) equal to 13.37908816 and -13.37908816.Subproblem 1
y + -12 = 13.37908816 Simplifying y + -12 = 13.37908816 Reorder the terms: -12 + y = 13.37908816 Solving -12 + y = 13.37908816 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 13.37908816 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.37908816 + 12 y = 13.37908816 + 12 Combine like terms: 13.37908816 + 12 = 25.37908816 y = 25.37908816 Simplifying y = 25.37908816Subproblem 2
y + -12 = -13.37908816 Simplifying y + -12 = -13.37908816 Reorder the terms: -12 + y = -13.37908816 Solving -12 + y = -13.37908816 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -13.37908816 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.37908816 + 12 y = -13.37908816 + 12 Combine like terms: -13.37908816 + 12 = -1.37908816 y = -1.37908816 Simplifying y = -1.37908816Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.37908816, -1.37908816}
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