x^2+4.2x=68.89

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Solution for x^2+4.2x=68.89 equation: 


Simplifying
x2 + 4.2x = 68.89

Reorder the terms:
4.2x + x2 = 68.89

Solving
4.2x + x2 = 68.89

Solving for variable 'x'.

Reorder the terms:
-68.89 + 4.2x + x2 = 68.89 + -68.89

Combine like terms: 68.89 + -68.89 = 0.00
-68.89 + 4.2x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '68.89' to each side of the equation.
-68.89 + 4.2x + 68.89 + x2 = 0.00 + 68.89

Reorder the terms:
-68.89 + 68.89 + 4.2x + x2 = 0.00 + 68.89

Combine like terms: -68.89 + 68.89 = 0.00
0.00 + 4.2x + x2 = 0.00 + 68.89
4.2x + x2 = 0.00 + 68.89

Combine like terms: 0.00 + 68.89 = 68.89
4.2x + x2 = 68.89

The x term is 4.2x.  Take half its coefficient (2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
4.2x + 4.41 + x2 = 68.89 + 4.41

Reorder the terms:
4.41 + 4.2x + x2 = 68.89 + 4.41

Combine like terms: 68.89 + 4.41 = 73.3
4.41 + 4.2x + x2 = 73.3

Factor a perfect square on the left side:
(x + 2.1)(x + 2.1) = 73.3

Calculate the square root of the right side: 8.561541917

Break this problem into two subproblems by setting 
(x + 2.1) equal to 8.561541917 and -8.561541917.


Subproblem 1
x + 2.1 = 8.561541917

Simplifying
x + 2.1 = 8.561541917

Reorder the terms:
2.1 + x = 8.561541917

Solving
2.1 + x = 8.561541917

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = 8.561541917 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = 8.561541917 + -2.1
x = 8.561541917 + -2.1

Combine like terms: 8.561541917 + -2.1 = 6.461541917
x = 6.461541917

Simplifying
x = 6.461541917


Subproblem 2
x + 2.1 = -8.561541917

Simplifying
x + 2.1 = -8.561541917

Reorder the terms:
2.1 + x = -8.561541917

Solving
2.1 + x = -8.561541917

Solving for variable 'x'.

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

Add '-2.1' to each side of the equation.
2.1 + -2.1 + x = -8.561541917 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + x = -8.561541917 + -2.1
x = -8.561541917 + -2.1

Combine like terms: -8.561541917 + -2.1 = -10.661541917
x = -10.661541917

Simplifying
x = -10.661541917


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.461541917, -10.661541917}

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