Y^2+7Y-10=0

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Solution for Y^2+7Y-10=0 equation: 


Simplifying
Y2 + 7Y + -10 = 0

Reorder the terms:
-10 + 7Y + Y2 = 0

Solving
-10 + 7Y + 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 + 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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