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Simplifying y2 + -12y + 5 = 0 Reorder the terms: 5 + -12y + y2 = 0 Solving 5 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -12y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -12y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -12y + y2 = 0 + -5 -12y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -12y + y2 = -5 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -5 + 36 Reorder the terms: 36 + -12y + y2 = -5 + 36 Combine like terms: -5 + 36 = 31 36 + -12y + y2 = 31 Factor a perfect square on the left side: (y + -6)(y + -6) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (y + -6) equal to 5.567764363 and -5.567764363.Subproblem 1
y + -6 = 5.567764363 Simplifying y + -6 = 5.567764363 Reorder the terms: -6 + y = 5.567764363 Solving -6 + y = 5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + y = 5.567764363 + 6 y = 5.567764363 + 6 Combine like terms: 5.567764363 + 6 = 11.567764363 y = 11.567764363 Simplifying y = 11.567764363Subproblem 2
y + -6 = -5.567764363 Simplifying y + -6 = -5.567764363 Reorder the terms: -6 + y = -5.567764363 Solving -6 + y = -5.567764363 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -5.567764363 + 6 Combine like terms: -6 + 6 = 0 0 + y = -5.567764363 + 6 y = -5.567764363 + 6 Combine like terms: -5.567764363 + 6 = 0.432235637 y = 0.432235637 Simplifying y = 0.432235637Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.567764363, 0.432235637}
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