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Simplifying y2 + -26y + 21 = 0 Reorder the terms: 21 + -26y + y2 = 0 Solving 21 + -26y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -26y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + -26y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -26y + y2 = 0 + -21 -26y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 -26y + y2 = -21 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 = -21 + 169 Reorder the terms: 169 + -26y + y2 = -21 + 169 Combine like terms: -21 + 169 = 148 169 + -26y + y2 = 148 Factor a perfect square on the left side: (y + -13)(y + -13) = 148 Calculate the square root of the right side: 12.165525061 Break this problem into two subproblems by setting (y + -13) equal to 12.165525061 and -12.165525061.Subproblem 1
y + -13 = 12.165525061 Simplifying y + -13 = 12.165525061 Reorder the terms: -13 + y = 12.165525061 Solving -13 + y = 12.165525061 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 = 12.165525061 + 13 Combine like terms: -13 + 13 = 0 0 + y = 12.165525061 + 13 y = 12.165525061 + 13 Combine like terms: 12.165525061 + 13 = 25.165525061 y = 25.165525061 Simplifying y = 25.165525061Subproblem 2
y + -13 = -12.165525061 Simplifying y + -13 = -12.165525061 Reorder the terms: -13 + y = -12.165525061 Solving -13 + y = -12.165525061 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 = -12.165525061 + 13 Combine like terms: -13 + 13 = 0 0 + y = -12.165525061 + 13 y = -12.165525061 + 13 Combine like terms: -12.165525061 + 13 = 0.834474939 y = 0.834474939 Simplifying y = 0.834474939Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.165525061, 0.834474939}
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