x*x-7x-22=0

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Solution for x*x-7x-22=0 equation: 


Simplifying
x * x + -7x + -22 = 0

Multiply x * x
x2 + -7x + -22 = 0

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

Solving
-22 + -7x + x2 = 0

Solving for variable 'x'.

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 = 9.352349955
x = 9.352349955

Simplifying
x = 9.352349955


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 = -2.352349955
x = -2.352349955

Simplifying
x = -2.352349955


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

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