0.7x^2-0.3x-1=0

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Solution for 0.7x^2-0.3x-1=0 equation: 


Simplifying
0.7x2 + -0.3x + -1 = 0

Reorder the terms:
-1 + -0.3x + 0.7x2 = 0

Solving
-1 + -0.3x + 0.7x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.7'.
-1.428571429 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + -0.4285714286x + 1.428571429 + x2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + -0.4285714286x + x2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + -0.4285714286x + x2 = 0 + 1.428571429
-0.4285714286x + x2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
-0.4285714286x + x2 = 1.428571429

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 1.428571429 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 1.428571429 + 0.04591836735

Combine like terms: 1.428571429 + 0.04591836735 = 1.47448979635
0.04591836735 + -0.4285714286x + x2 = 1.47448979635

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 1.47448979635

Calculate the square root of the right side: 1.214285714

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 1.214285714 and -1.214285714.


Subproblem 1
x + -0.2142857143 = 1.214285714

Simplifying
x + -0.2142857143 = 1.214285714

Reorder the terms:
-0.2142857143 + x = 1.214285714

Solving
-0.2142857143 + x = 1.214285714

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 1.214285714 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 1.214285714 + 0.2142857143
x = 1.214285714 + 0.2142857143

Combine like terms: 1.214285714 + 0.2142857143 = 1.4285714283
x = 1.4285714283

Simplifying
x = 1.4285714283


Subproblem 2
x + -0.2142857143 = -1.214285714

Simplifying
x + -0.2142857143 = -1.214285714

Reorder the terms:
-0.2142857143 + x = -1.214285714

Solving
-0.2142857143 + x = -1.214285714

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -1.214285714 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -1.214285714 + 0.2142857143
x = -1.214285714 + 0.2142857143

Combine like terms: -1.214285714 + 0.2142857143 = -0.9999999997
x = -0.9999999997

Simplifying
x = -0.9999999997


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4285714283, -0.9999999997}

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