.03x^2+0.7x-0.7=0

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Solution for .03x^2+0.7x-0.7=0 equation: 


Simplifying
0.03x2 + 0.7x + -0.7 = 0

Reorder the terms:
-0.7 + 0.7x + 0.03x2 = 0

Solving
-0.7 + 0.7x + 0.03x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.03'.
-23.33333333 + 23.33333333x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 23.33333333x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 23.33333333x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 23.33333333x + x2 = 0 + 23.33333333
23.33333333x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
23.33333333x + x2 = 23.33333333

The x term is 23.33333333x.  Take half its coefficient (11.66666667).
Square it (136.1111112) and add it to both sides.

Add '136.1111112' to each side of the equation.
23.33333333x + 136.1111112 + x2 = 23.33333333 + 136.1111112

Reorder the terms:
136.1111112 + 23.33333333x + x2 = 23.33333333 + 136.1111112

Combine like terms: 23.33333333 + 136.1111112 = 159.44444453
136.1111112 + 23.33333333x + x2 = 159.44444453

Factor a perfect square on the left side:
(x + 11.66666667)(x + 11.66666667) = 159.44444453

Calculate the square root of the right side: 12.627131287

Break this problem into two subproblems by setting 
(x + 11.66666667) equal to 12.627131287 and -12.627131287.


Subproblem 1
x + 11.66666667 = 12.627131287

Simplifying
x + 11.66666667 = 12.627131287

Reorder the terms:
11.66666667 + x = 12.627131287

Solving
11.66666667 + x = 12.627131287

Solving for variable 'x'.

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

Add '-11.66666667' to each side of the equation.
11.66666667 + -11.66666667 + x = 12.627131287 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = 12.627131287 + -11.66666667
x = 12.627131287 + -11.66666667

Combine like terms: 12.627131287 + -11.66666667 = 0.960464617
x = 0.960464617

Simplifying
x = 0.960464617


Subproblem 2
x + 11.66666667 = -12.627131287

Simplifying
x + 11.66666667 = -12.627131287

Reorder the terms:
11.66666667 + x = -12.627131287

Solving
11.66666667 + x = -12.627131287

Solving for variable 'x'.

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

Add '-11.66666667' to each side of the equation.
11.66666667 + -11.66666667 + x = -12.627131287 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = -12.627131287 + -11.66666667
x = -12.627131287 + -11.66666667

Combine like terms: -12.627131287 + -11.66666667 = -24.293797957
x = -24.293797957

Simplifying
x = -24.293797957


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.960464617, -24.293797957}

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