y^2+7*y=10

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Solution for y^2+7*y=10 equation: 


Simplifying
y2 + 7y = 10

Reorder the terms:
7y + y2 = 10

Solving
7y + y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 7y + y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 7y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 7y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + 7y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7y + y2 = 0 + 10
7y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
7y + y2 = 10

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = 10 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7y + y2 = 22.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(y + 3.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
y + 3.5 = 4.716990566

Simplifying
y + 3.5 = 4.716990566

Reorder the terms:
3.5 + y = 4.716990566

Solving
3.5 + y = 4.716990566

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 4.716990566 + -3.5
y = 4.716990566 + -3.5

Combine like terms: 4.716990566 + -3.5 = 1.216990566
y = 1.216990566

Simplifying
y = 1.216990566


Subproblem 2
y + 3.5 = -4.716990566

Simplifying
y + 3.5 = -4.716990566

Reorder the terms:
3.5 + y = -4.716990566

Solving
3.5 + y = -4.716990566

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -4.716990566 + -3.5
y = -4.716990566 + -3.5

Combine like terms: -4.716990566 + -3.5 = -8.216990566
y = -8.216990566

Simplifying
y = -8.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.216990566, -8.216990566}

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