y^2+11y=49

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Solution for y^2+11y=49 equation:


Simplifying
y2 + 11y = 49

Reorder the terms:
11y + y2 = 49

Solving
11y + y2 = 49

Solving for variable 'y'.

Reorder the terms:
-49 + 11y + y2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 11y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + 11y + 49 + y2 = 0 + 49

Reorder the terms:
-49 + 49 + 11y + y2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + 11y + y2 = 0 + 49
11y + y2 = 0 + 49

Combine like terms: 0 + 49 = 49
11y + y2 = 49

The y term is 11y.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11y + 30.25 + y2 = 49 + 30.25

Reorder the terms:
30.25 + 11y + y2 = 49 + 30.25

Combine like terms: 49 + 30.25 = 79.25
30.25 + 11y + y2 = 79.25

Factor a perfect square on the left side:
(y + 5.5)(y + 5.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(y + 5.5) equal to 8.902246907 and -8.902246907.

Subproblem 1

y + 5.5 = 8.902246907 Simplifying y + 5.5 = 8.902246907 Reorder the terms: 5.5 + y = 8.902246907 Solving 5.5 + y = 8.902246907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = 8.902246907 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 8.902246907 + -5.5 y = 8.902246907 + -5.5 Combine like terms: 8.902246907 + -5.5 = 3.402246907 y = 3.402246907 Simplifying y = 3.402246907

Subproblem 2

y + 5.5 = -8.902246907 Simplifying y + 5.5 = -8.902246907 Reorder the terms: 5.5 + y = -8.902246907 Solving 5.5 + y = -8.902246907 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + y = -8.902246907 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -8.902246907 + -5.5 y = -8.902246907 + -5.5 Combine like terms: -8.902246907 + -5.5 = -14.402246907 y = -14.402246907 Simplifying y = -14.402246907

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.402246907, -14.402246907}

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