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Simplifying 0 = y2 + -34y + 144 Reorder the terms: 0 = 144 + -34y + y2 Solving 0 = 144 + -34y + y2 Solving for variable 'y'. Combine like terms: 0 + -144 = -144 -144 + 34y + -1y2 = 144 + -34y + y2 + -144 + 34y + -1y2 Reorder the terms: -144 + 34y + -1y2 = 144 + -144 + -34y + 34y + y2 + -1y2 Combine like terms: 144 + -144 = 0 -144 + 34y + -1y2 = 0 + -34y + 34y + y2 + -1y2 -144 + 34y + -1y2 = -34y + 34y + y2 + -1y2 Combine like terms: -34y + 34y = 0 -144 + 34y + -1y2 = 0 + y2 + -1y2 -144 + 34y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -144 + 34y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 144 + -34y + y2 = 0 Move the constant term to the right: Add '-144' to each side of the equation. 144 + -34y + -144 + y2 = 0 + -144 Reorder the terms: 144 + -144 + -34y + y2 = 0 + -144 Combine like terms: 144 + -144 = 0 0 + -34y + y2 = 0 + -144 -34y + y2 = 0 + -144 Combine like terms: 0 + -144 = -144 -34y + y2 = -144 The y term is -34y. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34y + 289 + y2 = -144 + 289 Reorder the terms: 289 + -34y + y2 = -144 + 289 Combine like terms: -144 + 289 = 145 289 + -34y + y2 = 145 Factor a perfect square on the left side: (y + -17)(y + -17) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (y + -17) equal to 12.041594579 and -12.041594579.Subproblem 1
y + -17 = 12.041594579 Simplifying y + -17 = 12.041594579 Reorder the terms: -17 + y = 12.041594579 Solving -17 + y = 12.041594579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = 12.041594579 + 17 Combine like terms: -17 + 17 = 0 0 + y = 12.041594579 + 17 y = 12.041594579 + 17 Combine like terms: 12.041594579 + 17 = 29.041594579 y = 29.041594579 Simplifying y = 29.041594579Subproblem 2
y + -17 = -12.041594579 Simplifying y + -17 = -12.041594579 Reorder the terms: -17 + y = -12.041594579 Solving -17 + y = -12.041594579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = -12.041594579 + 17 Combine like terms: -17 + 17 = 0 0 + y = -12.041594579 + 17 y = -12.041594579 + 17 Combine like terms: -12.041594579 + 17 = 4.958405421 y = 4.958405421 Simplifying y = 4.958405421Solution
The solution to the problem is based on the solutions from the subproblems. y = {29.041594579, 4.958405421}
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