1.6x^2-1.31x-14.7=0

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Solution for 1.6x^2-1.31x-14.7=0 equation: 


Simplifying
1.6x2 + -1.31x + -14.7 = 0

Reorder the terms:
-14.7 + -1.31x + 1.6x2 = 0

Solving
-14.7 + -1.31x + 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'.
-9.1875 + -0.81875x + x2 = 0

Move the constant term to the right:

Add '9.1875' to each side of the equation.
-9.1875 + -0.81875x + 9.1875 + x2 = 0 + 9.1875

Reorder the terms:
-9.1875 + 9.1875 + -0.81875x + x2 = 0 + 9.1875

Combine like terms: -9.1875 + 9.1875 = 0.0000
0.0000 + -0.81875x + x2 = 0 + 9.1875
-0.81875x + x2 = 0 + 9.1875

Combine like terms: 0 + 9.1875 = 9.1875
-0.81875x + x2 = 9.1875

The x term is -0.81875x.  Take half its coefficient (-0.409375).
Square it (0.1675878906) and add it to both sides.

Add '0.1675878906' to each side of the equation.
-0.81875x + 0.1675878906 + x2 = 9.1875 + 0.1675878906

Reorder the terms:
0.1675878906 + -0.81875x + x2 = 9.1875 + 0.1675878906

Combine like terms: 9.1875 + 0.1675878906 = 9.3550878906
0.1675878906 + -0.81875x + x2 = 9.3550878906

Factor a perfect square on the left side:
(x + -0.409375)(x + -0.409375) = 9.3550878906

Calculate the square root of the right side: 3.058608816

Break this problem into two subproblems by setting 
(x + -0.409375) equal to 3.058608816 and -3.058608816.


Subproblem 1
x + -0.409375 = 3.058608816

Simplifying
x + -0.409375 = 3.058608816

Reorder the terms:
-0.409375 + x = 3.058608816

Solving
-0.409375 + x = 3.058608816

Solving for variable 'x'.

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

Add '0.409375' to each side of the equation.
-0.409375 + 0.409375 + x = 3.058608816 + 0.409375

Combine like terms: -0.409375 + 0.409375 = 0.000000
0.000000 + x = 3.058608816 + 0.409375
x = 3.058608816 + 0.409375

Combine like terms: 3.058608816 + 0.409375 = 3.467983816
x = 3.467983816

Simplifying
x = 3.467983816


Subproblem 2
x + -0.409375 = -3.058608816

Simplifying
x + -0.409375 = -3.058608816

Reorder the terms:
-0.409375 + x = -3.058608816

Solving
-0.409375 + x = -3.058608816

Solving for variable 'x'.

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

Add '0.409375' to each side of the equation.
-0.409375 + 0.409375 + x = -3.058608816 + 0.409375

Combine like terms: -0.409375 + 0.409375 = 0.000000
0.000000 + x = -3.058608816 + 0.409375
x = -3.058608816 + 0.409375

Combine like terms: -3.058608816 + 0.409375 = -2.649233816
x = -2.649233816

Simplifying
x = -2.649233816


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.467983816, -2.649233816}

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