-1.6x^2+10x-10=0

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Solution for -1.6x^2+10x-10=0 equation: 


Simplifying
-1.6x2 + 10x + -10 = 0

Reorder the terms:
-10 + 10x + -1.6x2 = 0

Solving
-10 + 10x + -1.6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.6 the coefficient of the squared term: 

Divide each side by '-1.6'.
6.25 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -6.25x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -6.25x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -6.25x + x2 = 0 + -6.25
-6.25x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-6.25x + x2 = -6.25

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -6.25 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -6.25 + 9.765625

Combine like terms: -6.25 + 9.765625 = 3.515625
9.765625 + -6.25x + x2 = 3.515625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 3.515625

Calculate the square root of the right side: 1.875

Break this problem into two subproblems by setting 
(x + -3.125) equal to 1.875 and -1.875.


Subproblem 1
x + -3.125 = 1.875

Simplifying
x + -3.125 = 1.875

Reorder the terms:
-3.125 + x = 1.875

Solving
-3.125 + x = 1.875

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 1.875 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 1.875 + 3.125
x = 1.875 + 3.125

Combine like terms: 1.875 + 3.125 = 5
x = 5

Simplifying
x = 5


Subproblem 2
x + -3.125 = -1.875

Simplifying
x + -3.125 = -1.875

Reorder the terms:
-3.125 + x = -1.875

Solving
-3.125 + x = -1.875

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -1.875 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -1.875 + 3.125
x = -1.875 + 3.125

Combine like terms: -1.875 + 3.125 = 1.25
x = 1.25

Simplifying
x = 1.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, 1.25}

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