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Simplifying y2 + 12y + 10 = 0 Reorder the terms: 10 + 12y + y2 = 0 Solving 10 + 12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 12y + -10 + y2 = 0 + -10 Reorder the terms: 10 + -10 + 12y + y2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 12y + y2 = 0 + -10 12y + y2 = 0 + -10 Combine like terms: 0 + -10 = -10 12y + y2 = -10 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 = -10 + 36 Reorder the terms: 36 + 12y + y2 = -10 + 36 Combine like terms: -10 + 36 = 26 36 + 12y + y2 = 26 Factor a perfect square on the left side: (y + 6)(y + 6) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (y + 6) equal to 5.099019514 and -5.099019514.Subproblem 1
y + 6 = 5.099019514 Simplifying y + 6 = 5.099019514 Reorder the terms: 6 + y = 5.099019514 Solving 6 + y = 5.099019514 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 = 5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + y = 5.099019514 + -6 y = 5.099019514 + -6 Combine like terms: 5.099019514 + -6 = -0.900980486 y = -0.900980486 Simplifying y = -0.900980486Subproblem 2
y + 6 = -5.099019514 Simplifying y + 6 = -5.099019514 Reorder the terms: 6 + y = -5.099019514 Solving 6 + y = -5.099019514 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 = -5.099019514 + -6 Combine like terms: 6 + -6 = 0 0 + y = -5.099019514 + -6 y = -5.099019514 + -6 Combine like terms: -5.099019514 + -6 = -11.099019514 y = -11.099019514 Simplifying y = -11.099019514Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.900980486, -11.099019514}
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