x^2+5.6x=8.16

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Solution for x^2+5.6x=8.16 equation: 


Simplifying
x2 + 5.6x = 8.16

Reorder the terms:
5.6x + x2 = 8.16

Solving
5.6x + x2 = 8.16

Solving for variable 'x'.

Reorder the terms:
-8.16 + 5.6x + x2 = 8.16 + -8.16

Combine like terms: 8.16 + -8.16 = 0.00
-8.16 + 5.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '8.16' to each side of the equation.
-8.16 + 5.6x + 8.16 + x2 = 0.00 + 8.16

Reorder the terms:
-8.16 + 8.16 + 5.6x + x2 = 0.00 + 8.16

Combine like terms: -8.16 + 8.16 = 0.00
0.00 + 5.6x + x2 = 0.00 + 8.16
5.6x + x2 = 0.00 + 8.16

Combine like terms: 0.00 + 8.16 = 8.16
5.6x + x2 = 8.16

The x term is 5.6x.  Take half its coefficient (2.8).
Square it (7.84) and add it to both sides.

Add '7.84' to each side of the equation.
5.6x + 7.84 + x2 = 8.16 + 7.84

Reorder the terms:
7.84 + 5.6x + x2 = 8.16 + 7.84

Combine like terms: 8.16 + 7.84 = 16
7.84 + 5.6x + x2 = 16

Factor a perfect square on the left side:
(x + 2.8)(x + 2.8) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + 2.8) equal to 4 and -4.


Subproblem 1
x + 2.8 = 4

Simplifying
x + 2.8 = 4

Reorder the terms:
2.8 + x = 4

Solving
2.8 + x = 4

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = 4 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = 4 + -2.8
x = 4 + -2.8

Combine like terms: 4 + -2.8 = 1.2
x = 1.2

Simplifying
x = 1.2


Subproblem 2
x + 2.8 = -4

Simplifying
x + 2.8 = -4

Reorder the terms:
2.8 + x = -4

Solving
2.8 + x = -4

Solving for variable 'x'.

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

Add '-2.8' to each side of the equation.
2.8 + -2.8 + x = -4 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + x = -4 + -2.8
x = -4 + -2.8

Combine like terms: -4 + -2.8 = -6.8
x = -6.8

Simplifying
x = -6.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2, -6.8}

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