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Simplifying y2 + -26y + 89 = 0 Reorder the terms: 89 + -26y + y2 = 0 Solving 89 + -26y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-89' to each side of the equation. 89 + -26y + -89 + y2 = 0 + -89 Reorder the terms: 89 + -89 + -26y + y2 = 0 + -89 Combine like terms: 89 + -89 = 0 0 + -26y + y2 = 0 + -89 -26y + y2 = 0 + -89 Combine like terms: 0 + -89 = -89 -26y + y2 = -89 The y term is -26y. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26y + 169 + y2 = -89 + 169 Reorder the terms: 169 + -26y + y2 = -89 + 169 Combine like terms: -89 + 169 = 80 169 + -26y + y2 = 80 Factor a perfect square on the left side: (y + -13)(y + -13) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (y + -13) equal to 8.94427191 and -8.94427191.Subproblem 1
y + -13 = 8.94427191 Simplifying y + -13 = 8.94427191 Reorder the terms: -13 + y = 8.94427191 Solving -13 + y = 8.94427191 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = 8.94427191 + 13 Combine like terms: -13 + 13 = 0 0 + y = 8.94427191 + 13 y = 8.94427191 + 13 Combine like terms: 8.94427191 + 13 = 21.94427191 y = 21.94427191 Simplifying y = 21.94427191Subproblem 2
y + -13 = -8.94427191 Simplifying y + -13 = -8.94427191 Reorder the terms: -13 + y = -8.94427191 Solving -13 + y = -8.94427191 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = -8.94427191 + 13 Combine like terms: -13 + 13 = 0 0 + y = -8.94427191 + 13 y = -8.94427191 + 13 Combine like terms: -8.94427191 + 13 = 4.05572809 y = 4.05572809 Simplifying y = 4.05572809Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.94427191, 4.05572809}
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