y=y^2+3y+10

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Solution for y=y^2+3y+10 equation: 


Simplifying
y = y2 + 3y + 10

Reorder the terms:
y = 10 + 3y + y2

Solving
y = 10 + 3y + y2

Solving for variable 'y'.

Reorder the terms:
-10 + y + -3y + -1y2 = 10 + 3y + y2 + -10 + -3y + -1y2

Combine like terms: y + -3y = -2y
-10 + -2y + -1y2 = 10 + 3y + y2 + -10 + -3y + -1y2

Reorder the terms:
-10 + -2y + -1y2 = 10 + -10 + 3y + -3y + y2 + -1y2

Combine like terms: 10 + -10 = 0
-10 + -2y + -1y2 = 0 + 3y + -3y + y2 + -1y2
-10 + -2y + -1y2 = 3y + -3y + y2 + -1y2

Combine like terms: 3y + -3y = 0
-10 + -2y + -1y2 = 0 + y2 + -1y2
-10 + -2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-10 + -2y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 2y + y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
10 + 2y + y2 = 0

Solving
10 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 2y + -10 + y2 = 0 + -10

Reorder the terms:
10 + -10 + 2y + y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 2y + y2 = 0 + -10
2y + y2 = 0 + -10

Combine like terms: 0 + -10 = -10
2y + y2 = -10

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -10 + 1

Reorder the terms:
1 + 2y + y2 = -10 + 1

Combine like terms: -10 + 1 = -9
1 + 2y + y2 = -9

Factor a perfect square on the left side:
(y + 1)(y + 1) = -9

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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