0.3x^2+5x-7=0

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Solution for 0.3x^2+5x-7=0 equation: 


Simplifying
0.3x2 + 5x + -7 = 0

Reorder the terms:
-7 + 5x + 0.3x2 = 0

Solving
-7 + 5x + 0.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.3'.
-23.33333333 + 16.66666667x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 16.66666667x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 16.66666667x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 16.66666667x + x2 = 0 + 23.33333333
16.66666667x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
16.66666667x + x2 = 23.33333333

The x term is 16.66666667x.  Take half its coefficient (8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
16.66666667x + 69.44444447 + x2 = 23.33333333 + 69.44444447

Reorder the terms:
69.44444447 + 16.66666667x + x2 = 23.33333333 + 69.44444447

Combine like terms: 23.33333333 + 69.44444447 = 92.7777778
69.44444447 + 16.66666667x + x2 = 92.7777778

Factor a perfect square on the left side:
(x + 8.333333335)(x + 8.333333335) = 92.7777778

Calculate the square root of the right side: 9.632122186

Break this problem into two subproblems by setting 
(x + 8.333333335) equal to 9.632122186 and -9.632122186.


Subproblem 1
x + 8.333333335 = 9.632122186

Simplifying
x + 8.333333335 = 9.632122186

Reorder the terms:
8.333333335 + x = 9.632122186

Solving
8.333333335 + x = 9.632122186

Solving for variable 'x'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + x = 9.632122186 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + x = 9.632122186 + -8.333333335
x = 9.632122186 + -8.333333335

Combine like terms: 9.632122186 + -8.333333335 = 1.298788851
x = 1.298788851

Simplifying
x = 1.298788851


Subproblem 2
x + 8.333333335 = -9.632122186

Simplifying
x + 8.333333335 = -9.632122186

Reorder the terms:
8.333333335 + x = -9.632122186

Solving
8.333333335 + x = -9.632122186

Solving for variable 'x'.

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

Add '-8.333333335' to each side of the equation.
8.333333335 + -8.333333335 + x = -9.632122186 + -8.333333335

Combine like terms: 8.333333335 + -8.333333335 = 0.000000000
0.000000000 + x = -9.632122186 + -8.333333335
x = -9.632122186 + -8.333333335

Combine like terms: -9.632122186 + -8.333333335 = -17.965455521
x = -17.965455521

Simplifying
x = -17.965455521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.298788851, -17.965455521}

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