0.3x^2+0.7x=0.25

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Solution for 0.3x^2+0.7x=0.25 equation: 


Simplifying
0.3x2 + 0.7x = 0.25

Reorder the terms:
0.7x + 0.3x2 = 0.25

Solving
0.7x + 0.3x2 = 0.25

Solving for variable 'x'.

Reorder the terms:
-0.25 + 0.7x + 0.3x2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + 0.7x + 0.3x2 = 0.00

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

Divide each side by '0.3'.
-0.8333333333 + 2.333333333x + x2 = 0.0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2.333333333x + 0.8333333333 + x2 = 0.0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2.333333333x + x2 = 0.0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2.333333333x + x2 = 0.0 + 0.8333333333
2.333333333x + x2 = 0.0 + 0.8333333333

Combine like terms: 0.0 + 0.8333333333 = 0.8333333333
2.333333333x + x2 = 0.8333333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 0.8333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 0.8333333333 + 1.361111112

Combine like terms: 0.8333333333 + 1.361111112 = 2.1944444453
1.361111112 + 2.333333333x + x2 = 2.1944444453

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 2.1944444453

Calculate the square root of the right side: 1.481365737

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 1.481365737 and -1.481365737.


Subproblem 1
x + 1.166666667 = 1.481365737

Simplifying
x + 1.166666667 = 1.481365737

Reorder the terms:
1.166666667 + x = 1.481365737

Solving
1.166666667 + x = 1.481365737

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 1.481365737 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 1.481365737 + -1.166666667
x = 1.481365737 + -1.166666667

Combine like terms: 1.481365737 + -1.166666667 = 0.31469907
x = 0.31469907

Simplifying
x = 0.31469907


Subproblem 2
x + 1.166666667 = -1.481365737

Simplifying
x + 1.166666667 = -1.481365737

Reorder the terms:
1.166666667 + x = -1.481365737

Solving
1.166666667 + x = -1.481365737

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -1.481365737 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -1.481365737 + -1.166666667
x = -1.481365737 + -1.166666667

Combine like terms: -1.481365737 + -1.166666667 = -2.648032404
x = -2.648032404

Simplifying
x = -2.648032404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.31469907, -2.648032404}

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