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Simplifying y2 + 26y = 3 Reorder the terms: 26y + y2 = 3 Solving 26y + y2 = 3 Solving for variable 'y'. Reorder the terms: -3 + 26y + y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 26y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 26y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 26y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 26y + y2 = 0 + 3 26y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 26y + y2 = 3 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 = 3 + 169 Reorder the terms: 169 + 26y + y2 = 3 + 169 Combine like terms: 3 + 169 = 172 169 + 26y + y2 = 172 Factor a perfect square on the left side: (y + 13)(y + 13) = 172 Calculate the square root of the right side: 13.114877049 Break this problem into two subproblems by setting (y + 13) equal to 13.114877049 and -13.114877049.Subproblem 1
y + 13 = 13.114877049 Simplifying y + 13 = 13.114877049 Reorder the terms: 13 + y = 13.114877049 Solving 13 + y = 13.114877049 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 = 13.114877049 + -13 Combine like terms: 13 + -13 = 0 0 + y = 13.114877049 + -13 y = 13.114877049 + -13 Combine like terms: 13.114877049 + -13 = 0.114877049 y = 0.114877049 Simplifying y = 0.114877049Subproblem 2
y + 13 = -13.114877049 Simplifying y + 13 = -13.114877049 Reorder the terms: 13 + y = -13.114877049 Solving 13 + y = -13.114877049 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 = -13.114877049 + -13 Combine like terms: 13 + -13 = 0 0 + y = -13.114877049 + -13 y = -13.114877049 + -13 Combine like terms: -13.114877049 + -13 = -26.114877049 y = -26.114877049 Simplifying y = -26.114877049Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.114877049, -26.114877049}
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