(x*x)+(5x)=8

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Solution for (x*x)+(5x)=8 equation: 


Simplifying
(x * x) + (5x) = 8

Multiply x * x
(x2) + (5x) = 8
x2 + (5x) = 8

Reorder the terms:
(5x) + x2 = 8

Solving
(5x) + x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + (5x) + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + (5x) + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + (5x) + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + (5x) + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + (5x) + x2 = 0 + 8
(5x) + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
(5x) + x2 = 8

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 = 8 + 6.25

Reorder the terms:
6.25 + (5x) + x2 = 8 + 6.25

Combine like terms: 8 + 6.25 = 14.25
6.25 + (5x) + x2 = 14.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + 2.5 = 3.774917218

Simplifying
x + 2.5 = 3.774917218

Reorder the terms:
2.5 + x = 3.774917218

Solving
2.5 + x = 3.774917218

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 = 3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.774917218 + -2.5
x = 3.774917218 + -2.5

Combine like terms: 3.774917218 + -2.5 = 1.274917218
x = 1.274917218

Simplifying
x = 1.274917218


Subproblem 2
x + 2.5 = -3.774917218

Simplifying
x + 2.5 = -3.774917218

Reorder the terms:
2.5 + x = -3.774917218

Solving
2.5 + x = -3.774917218

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 = -3.774917218 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.774917218 + -2.5
x = -3.774917218 + -2.5

Combine like terms: -3.774917218 + -2.5 = -6.274917218
x = -6.274917218

Simplifying
x = -6.274917218


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.274917218, -6.274917218}

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