1.6x^2-1.61x-10.5=0

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Solution for 1.6x^2-1.61x-10.5=0 equation: 


Simplifying
1.6x2 + -1.61x + -10.5 = 0

Reorder the terms:
-10.5 + -1.61x + 1.6x2 = 0

Solving
-10.5 + -1.61x + 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'.
-6.5625 + -1.00625x + x2 = 0

Move the constant term to the right:

Add '6.5625' to each side of the equation.
-6.5625 + -1.00625x + 6.5625 + x2 = 0 + 6.5625

Reorder the terms:
-6.5625 + 6.5625 + -1.00625x + x2 = 0 + 6.5625

Combine like terms: -6.5625 + 6.5625 = 0.0000
0.0000 + -1.00625x + x2 = 0 + 6.5625
-1.00625x + x2 = 0 + 6.5625

Combine like terms: 0 + 6.5625 = 6.5625
-1.00625x + x2 = 6.5625

The x term is -1.00625x.  Take half its coefficient (-0.503125).
Square it (0.2531347656) and add it to both sides.

Add '0.2531347656' to each side of the equation.
-1.00625x + 0.2531347656 + x2 = 6.5625 + 0.2531347656

Reorder the terms:
0.2531347656 + -1.00625x + x2 = 6.5625 + 0.2531347656

Combine like terms: 6.5625 + 0.2531347656 = 6.8156347656
0.2531347656 + -1.00625x + x2 = 6.8156347656

Factor a perfect square on the left side:
(x + -0.503125)(x + -0.503125) = 6.8156347656

Calculate the square root of the right side: 2.61067707

Break this problem into two subproblems by setting 
(x + -0.503125) equal to 2.61067707 and -2.61067707.


Subproblem 1
x + -0.503125 = 2.61067707

Simplifying
x + -0.503125 = 2.61067707

Reorder the terms:
-0.503125 + x = 2.61067707

Solving
-0.503125 + x = 2.61067707

Solving for variable 'x'.

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

Add '0.503125' to each side of the equation.
-0.503125 + 0.503125 + x = 2.61067707 + 0.503125

Combine like terms: -0.503125 + 0.503125 = 0.000000
0.000000 + x = 2.61067707 + 0.503125
x = 2.61067707 + 0.503125

Combine like terms: 2.61067707 + 0.503125 = 3.11380207
x = 3.11380207

Simplifying
x = 3.11380207


Subproblem 2
x + -0.503125 = -2.61067707

Simplifying
x + -0.503125 = -2.61067707

Reorder the terms:
-0.503125 + x = -2.61067707

Solving
-0.503125 + x = -2.61067707

Solving for variable 'x'.

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

Add '0.503125' to each side of the equation.
-0.503125 + 0.503125 + x = -2.61067707 + 0.503125

Combine like terms: -0.503125 + 0.503125 = 0.000000
0.000000 + x = -2.61067707 + 0.503125
x = -2.61067707 + 0.503125

Combine like terms: -2.61067707 + 0.503125 = -2.10755207
x = -2.10755207

Simplifying
x = -2.10755207


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.11380207, -2.10755207}

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