x*x+5x=9

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Solution for x*x+5x=9 equation: 


Simplifying
x * x + 5x = 9

Multiply x * x
x2 + 5x = 9

Reorder the terms:
5x + x2 = 9

Solving
5x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + 5x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 5x + x2 = 0 + 9
5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
5x + x2 = 9

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 9 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 9 + 6.25

Combine like terms: 9 + 6.25 = 15.25
6.25 + 5x + x2 = 15.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + 2.5 = 3.905124838

Simplifying
x + 2.5 = 3.905124838

Reorder the terms:
2.5 + x = 3.905124838

Solving
2.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.905124838 + -2.5
x = 3.905124838 + -2.5

Combine like terms: 3.905124838 + -2.5 = 1.405124838
x = 1.405124838

Simplifying
x = 1.405124838


Subproblem 2
x + 2.5 = -3.905124838

Simplifying
x + 2.5 = -3.905124838

Reorder the terms:
2.5 + x = -3.905124838

Solving
2.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.905124838 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.905124838 + -2.5
x = -3.905124838 + -2.5

Combine like terms: -3.905124838 + -2.5 = -6.405124838
x = -6.405124838

Simplifying
x = -6.405124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.405124838, -6.405124838}

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