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Simplifying y2 + -26y + 17 = 0 Reorder the terms: 17 + -26y + y2 = 0 Solving 17 + -26y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -26y + -17 + y2 = 0 + -17 Reorder the terms: 17 + -17 + -26y + y2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -26y + y2 = 0 + -17 -26y + y2 = 0 + -17 Combine like terms: 0 + -17 = -17 -26y + y2 = -17 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 = -17 + 169 Reorder the terms: 169 + -26y + y2 = -17 + 169 Combine like terms: -17 + 169 = 152 169 + -26y + y2 = 152 Factor a perfect square on the left side: (y + -13)(y + -13) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (y + -13) equal to 12.328828006 and -12.328828006.Subproblem 1
y + -13 = 12.328828006 Simplifying y + -13 = 12.328828006 Reorder the terms: -13 + y = 12.328828006 Solving -13 + y = 12.328828006 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 = 12.328828006 + 13 Combine like terms: -13 + 13 = 0 0 + y = 12.328828006 + 13 y = 12.328828006 + 13 Combine like terms: 12.328828006 + 13 = 25.328828006 y = 25.328828006 Simplifying y = 25.328828006Subproblem 2
y + -13 = -12.328828006 Simplifying y + -13 = -12.328828006 Reorder the terms: -13 + y = -12.328828006 Solving -13 + y = -12.328828006 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 = -12.328828006 + 13 Combine like terms: -13 + 13 = 0 0 + y = -12.328828006 + 13 y = -12.328828006 + 13 Combine like terms: -12.328828006 + 13 = 0.671171994 y = 0.671171994 Simplifying y = 0.671171994Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.328828006, 0.671171994}
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