y^2+18y+28=0

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Solution for y^2+18y+28=0 equation:


Simplifying
y2 + 18y + 28 = 0

Reorder the terms:
28 + 18y + y2 = 0

Solving
28 + 18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 18y + -28 + y2 = 0 + -28

Reorder the terms:
28 + -28 + 18y + y2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 18y + y2 = 0 + -28
18y + y2 = 0 + -28

Combine like terms: 0 + -28 = -28
18y + y2 = -28

The y term is 18y.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18y + 81 + y2 = -28 + 81

Reorder the terms:
81 + 18y + y2 = -28 + 81

Combine like terms: -28 + 81 = 53
81 + 18y + y2 = 53

Factor a perfect square on the left side:
(y + 9)(y + 9) = 53

Calculate the square root of the right side: 7.280109889

Break this problem into two subproblems by setting 
(y + 9) equal to 7.280109889 and -7.280109889.

Subproblem 1

y + 9 = 7.280109889 Simplifying y + 9 = 7.280109889 Reorder the terms: 9 + y = 7.280109889 Solving 9 + y = 7.280109889 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 7.280109889 + -9 Combine like terms: 9 + -9 = 0 0 + y = 7.280109889 + -9 y = 7.280109889 + -9 Combine like terms: 7.280109889 + -9 = -1.719890111 y = -1.719890111 Simplifying y = -1.719890111

Subproblem 2

y + 9 = -7.280109889 Simplifying y + 9 = -7.280109889 Reorder the terms: 9 + y = -7.280109889 Solving 9 + y = -7.280109889 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = -7.280109889 + -9 Combine like terms: 9 + -9 = 0 0 + y = -7.280109889 + -9 y = -7.280109889 + -9 Combine like terms: -7.280109889 + -9 = -16.280109889 y = -16.280109889 Simplifying y = -16.280109889

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-1.719890111, -16.280109889}

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