0.795=-.0074x^2+0.2505x+0.1271

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Solution for 0.795=-.0074x^2+0.2505x+0.1271 equation:


Simplifying
0.795 = -0.0074x2 + 0.2505x + 0.1271

Reorder the terms:
0.795 = 0.1271 + 0.2505x + -0.0074x2

Solving
0.795 = 0.1271 + 0.2505x + -0.0074x2

Solving for variable 'x'.

Combine like terms: 0.795 + -0.1271 = 0.6679
0.6679 + -0.2505x + 0.0074x2 = 0.1271 + 0.2505x + -0.0074x2 + -0.1271 + -0.2505x + 0.0074x2

Reorder the terms:
0.6679 + -0.2505x + 0.0074x2 = 0.1271 + -0.1271 + 0.2505x + -0.2505x + -0.0074x2 + 0.0074x2

Combine like terms: 0.1271 + -0.1271 = 0.0000
0.6679 + -0.2505x + 0.0074x2 = 0.0000 + 0.2505x + -0.2505x + -0.0074x2 + 0.0074x2
0.6679 + -0.2505x + 0.0074x2 = 0.2505x + -0.2505x + -0.0074x2 + 0.0074x2

Combine like terms: 0.2505x + -0.2505x = 0.0000
0.6679 + -0.2505x + 0.0074x2 = 0.0000 + -0.0074x2 + 0.0074x2
0.6679 + -0.2505x + 0.0074x2 = -0.0074x2 + 0.0074x2

Combine like terms: -0.0074x2 + 0.0074x2 = 0.0000
0.6679 + -0.2505x + 0.0074x2 = 0.0000

Begin completing the square.  Divide all terms by
0.0074 the coefficient of the squared term: 

Divide each side by '0.0074'.
90.25675676 + -33.85135135x + x2 = 0

Move the constant term to the right:

Add '-90.25675676' to each side of the equation.
90.25675676 + -33.85135135x + -90.25675676 + x2 = 0 + -90.25675676

Reorder the terms:
90.25675676 + -90.25675676 + -33.85135135x + x2 = 0 + -90.25675676

Combine like terms: 90.25675676 + -90.25675676 = 0.00000000
0.00000000 + -33.85135135x + x2 = 0 + -90.25675676
-33.85135135x + x2 = 0 + -90.25675676

Combine like terms: 0 + -90.25675676 = -90.25675676
-33.85135135x + x2 = -90.25675676

The x term is -33.85135135x.  Take half its coefficient (-16.92567568).
Square it (286.4784972) and add it to both sides.

Add '286.4784972' to each side of the equation.
-33.85135135x + 286.4784972 + x2 = -90.25675676 + 286.4784972

Reorder the terms:
286.4784972 + -33.85135135x + x2 = -90.25675676 + 286.4784972

Combine like terms: -90.25675676 + 286.4784972 = 196.22174044
286.4784972 + -33.85135135x + x2 = 196.22174044

Factor a perfect square on the left side:
(x + -16.92567568)(x + -16.92567568) = 196.22174044

Calculate the square root of the right side: 14.007917063

Break this problem into two subproblems by setting 
(x + -16.92567568) equal to 14.007917063 and -14.007917063.


Subproblem 1
x + -16.92567568 = 14.007917063

Simplifying
x + -16.92567568 = 14.007917063

Reorder the terms:
-16.92567568 + x = 14.007917063

Solving
-16.92567568 + x = 14.007917063

Solving for variable 'x'.

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

Add '16.92567568' to each side of the equation.
-16.92567568 + 16.92567568 + x = 14.007917063 + 16.92567568

Combine like terms: -16.92567568 + 16.92567568 = 0.00000000
0.00000000 + x = 14.007917063 + 16.92567568
x = 14.007917063 + 16.92567568

Combine like terms: 14.007917063 + 16.92567568 = 30.933592743
x = 30.933592743

Simplifying
x = 30.933592743


Subproblem 2
x + -16.92567568 = -14.007917063

Simplifying
x + -16.92567568 = -14.007917063

Reorder the terms:
-16.92567568 + x = -14.007917063

Solving
-16.92567568 + x = -14.007917063

Solving for variable 'x'.

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

Add '16.92567568' to each side of the equation.
-16.92567568 + 16.92567568 + x = -14.007917063 + 16.92567568

Combine like terms: -16.92567568 + 16.92567568 = 0.00000000
0.00000000 + x = -14.007917063 + 16.92567568
x = -14.007917063 + 16.92567568

Combine like terms: -14.007917063 + 16.92567568 = 2.917758617
x = 2.917758617

Simplifying
x = 2.917758617


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.933592743, 2.917758617}

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