x*x+7x=22

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Solution for x*x+7x=22 equation: 


Simplifying
x * x + 7x = 22

Multiply x * x
x2 + 7x = 22

Reorder the terms:
7x + x2 = 22

Solving
7x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-22 + 7x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-22 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + 7x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + 7x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 7x + x2 = 0 + 22
7x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
7x + x2 = 22

The x term is 7x.  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.
7x + 12.25 + x2 = 22 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 22 + 12.25

Combine like terms: 22 + 12.25 = 34.25
12.25 + 7x + x2 = 34.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(x + 3.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
x + 3.5 = 5.852349955

Simplifying
x + 3.5 = 5.852349955

Reorder the terms:
3.5 + x = 5.852349955

Solving
3.5 + x = 5.852349955

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 5.852349955 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 5.852349955 + -3.5
x = 5.852349955 + -3.5

Combine like terms: 5.852349955 + -3.5 = 2.352349955
x = 2.352349955

Simplifying
x = 2.352349955


Subproblem 2
x + 3.5 = -5.852349955

Simplifying
x + 3.5 = -5.852349955

Reorder the terms:
3.5 + x = -5.852349955

Solving
3.5 + x = -5.852349955

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -5.852349955 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -5.852349955 + -3.5
x = -5.852349955 + -3.5

Combine like terms: -5.852349955 + -3.5 = -9.352349955
x = -9.352349955

Simplifying
x = -9.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.352349955, -9.352349955}

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