0.4x^2+0.7x-0.7=0

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Solution for 0.4x^2+0.7x-0.7=0 equation: 


Simplifying
0.4x2 + 0.7x + -0.7 = 0

Reorder the terms:
-0.7 + 0.7x + 0.4x2 = 0

Solving
-0.7 + 0.7x + 0.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.4'.
-1.75 + 1.75x + x2 = 0

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 1.75x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 1.75x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 1.75x + x2 = 0 + 1.75
1.75x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
1.75x + x2 = 1.75

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 1.75 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 1.75 + 0.765625

Combine like terms: 1.75 + 0.765625 = 2.515625
0.765625 + 1.75x + x2 = 2.515625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.586072193 and -1.586072193.


Subproblem 1
x + 0.875 = 1.586072193

Simplifying
x + 0.875 = 1.586072193

Reorder the terms:
0.875 + x = 1.586072193

Solving
0.875 + x = 1.586072193

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 1.586072193 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 1.586072193 + -0.875
x = 1.586072193 + -0.875

Combine like terms: 1.586072193 + -0.875 = 0.711072193
x = 0.711072193

Simplifying
x = 0.711072193


Subproblem 2
x + 0.875 = -1.586072193

Simplifying
x + 0.875 = -1.586072193

Reorder the terms:
0.875 + x = -1.586072193

Solving
0.875 + x = -1.586072193

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -1.586072193 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -1.586072193 + -0.875
x = -1.586072193 + -0.875

Combine like terms: -1.586072193 + -0.875 = -2.461072193
x = -2.461072193

Simplifying
x = -2.461072193


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.711072193, -2.461072193}

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