0.003x^2+0.7x+8=0

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Solution for 0.003x^2+0.7x+8=0 equation: 


Simplifying
0.003x2 + 0.7x + 8 = 0

Reorder the terms:
8 + 0.7x + 0.003x2 = 0

Solving
8 + 0.7x + 0.003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.003 the coefficient of the squared term: 

Divide each side by '0.003'.
2666.666667 + 233.3333333x + x2 = 0

Move the constant term to the right:

Add '-2666.666667' to each side of the equation.
2666.666667 + 233.3333333x + -2666.666667 + x2 = 0 + -2666.666667

Reorder the terms:
2666.666667 + -2666.666667 + 233.3333333x + x2 = 0 + -2666.666667

Combine like terms: 2666.666667 + -2666.666667 = 0.000000
0.000000 + 233.3333333x + x2 = 0 + -2666.666667
233.3333333x + x2 = 0 + -2666.666667

Combine like terms: 0 + -2666.666667 = -2666.666667
233.3333333x + x2 = -2666.666667

The x term is 233.3333333x.  Take half its coefficient (116.6666667).
Square it (13611.11112) and add it to both sides.

Add '13611.11112' to each side of the equation.
233.3333333x + 13611.11112 + x2 = -2666.666667 + 13611.11112

Reorder the terms:
13611.11112 + 233.3333333x + x2 = -2666.666667 + 13611.11112

Combine like terms: -2666.666667 + 13611.11112 = 10944.444453
13611.11112 + 233.3333333x + x2 = 10944.444453

Factor a perfect square on the left side:
(x + 116.6666667)(x + 116.6666667) = 10944.444453

Calculate the square root of the right side: 104.615698884

Break this problem into two subproblems by setting 
(x + 116.6666667) equal to 104.615698884 and -104.615698884.


Subproblem 1
x + 116.6666667 = 104.615698884

Simplifying
x + 116.6666667 = 104.615698884

Reorder the terms:
116.6666667 + x = 104.615698884

Solving
116.6666667 + x = 104.615698884

Solving for variable 'x'.

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

Add '-116.6666667' to each side of the equation.
116.6666667 + -116.6666667 + x = 104.615698884 + -116.6666667

Combine like terms: 116.6666667 + -116.6666667 = 0.0000000
0.0000000 + x = 104.615698884 + -116.6666667
x = 104.615698884 + -116.6666667

Combine like terms: 104.615698884 + -116.6666667 = -12.050967816
x = -12.050967816

Simplifying
x = -12.050967816


Subproblem 2
x + 116.6666667 = -104.615698884

Simplifying
x + 116.6666667 = -104.615698884

Reorder the terms:
116.6666667 + x = -104.615698884

Solving
116.6666667 + x = -104.615698884

Solving for variable 'x'.

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

Add '-116.6666667' to each side of the equation.
116.6666667 + -116.6666667 + x = -104.615698884 + -116.6666667

Combine like terms: 116.6666667 + -116.6666667 = 0.0000000
0.0000000 + x = -104.615698884 + -116.6666667
x = -104.615698884 + -116.6666667

Combine like terms: -104.615698884 + -116.6666667 = -221.282365584
x = -221.282365584

Simplifying
x = -221.282365584


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-12.050967816, -221.282365584}

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