x^2+10x+4x+21=

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Solution for x^2+10x+4x+21= equation:


Simplifying
x2 + 10x + 4x + 21 = 0

Reorder the terms:
21 + 10x + 4x + x2 = 0

Combine like terms: 10x + 4x = 14x
21 + 14x + x2 = 0

Solving
21 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 14x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + 14x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 14x + x2 = 0 + -21
14x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
14x + x2 = -21

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -21 + 49

Reorder the terms:
49 + 14x + x2 = -21 + 49

Combine like terms: -21 + 49 = 28
49 + 14x + x2 = 28

Factor a perfect square on the left side:
(x + 7)(x + 7) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + 7) equal to 5.291502622 and -5.291502622.


Subproblem 1
x + 7 = 5.291502622

Simplifying
x + 7 = 5.291502622

Reorder the terms:
7 + x = 5.291502622

Solving
7 + x = 5.291502622

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 5.291502622 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.291502622 + -7
x = 5.291502622 + -7

Combine like terms: 5.291502622 + -7 = -1.708497378
x = -1.708497378

Simplifying
x = -1.708497378


Subproblem 2
x + 7 = -5.291502622

Simplifying
x + 7 = -5.291502622

Reorder the terms:
7 + x = -5.291502622

Solving
7 + x = -5.291502622

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -5.291502622 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.291502622 + -7
x = -5.291502622 + -7

Combine like terms: -5.291502622 + -7 = -12.291502622
x = -12.291502622

Simplifying
x = -12.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.708497378, -12.291502622}

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