x+7=16+3x+x^2

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Solution for x+7=16+3x+x^2 equation: 


Simplifying
x + 7 = 16 + 3x + x2

Reorder the terms:
7 + x = 16 + 3x + x2

Solving
7 + x = 16 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -16 + x + -3x + -1x2 = 16 + 3x + x2 + -16 + -3x + -1x2

Combine like terms: 7 + -16 = -9
-9 + x + -3x + -1x2 = 16 + 3x + x2 + -16 + -3x + -1x2

Combine like terms: x + -3x = -2x
-9 + -2x + -1x2 = 16 + 3x + x2 + -16 + -3x + -1x2

Reorder the terms:
-9 + -2x + -1x2 = 16 + -16 + 3x + -3x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-9 + -2x + -1x2 = 0 + 3x + -3x + x2 + -1x2
-9 + -2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-9 + -2x + -1x2 = 0 + x2 + -1x2
-9 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(9 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
9 + 2x + x2 = 0

Solving
9 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 2x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 2x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2x + x2 = 0 + -9
2x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
2x + x2 = -9

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

Add '1' to each side of the equation.
2x + 1 + x2 = -9 + 1

Reorder the terms:
1 + 2x + x2 = -9 + 1

Combine like terms: -9 + 1 = -8
1 + 2x + x2 = -8

Factor a perfect square on the left side:
(x + 1)(x + 1) = -8

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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