9.5-0.315x^2+0.743x=0

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Solution for 9.5-0.315x^2+0.743x=0 equation: 


Simplifying
9.5 + -0.315x2 + 0.743x = 0

Reorder the terms:
9.5 + 0.743x + -0.315x2 = 0

Solving
9.5 + 0.743x + -0.315x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.315 the coefficient of the squared term: 

Divide each side by '-0.315'.
-30.15873016 + -2.358730159x + x2 = 0

Move the constant term to the right:

Add '30.15873016' to each side of the equation.
-30.15873016 + -2.358730159x + 30.15873016 + x2 = 0 + 30.15873016

Reorder the terms:
-30.15873016 + 30.15873016 + -2.358730159x + x2 = 0 + 30.15873016

Combine like terms: -30.15873016 + 30.15873016 = 0.00000000
0.00000000 + -2.358730159x + x2 = 0 + 30.15873016
-2.358730159x + x2 = 0 + 30.15873016

Combine like terms: 0 + 30.15873016 = 30.15873016
-2.358730159x + x2 = 30.15873016

The x term is -2.358730159x.  Take half its coefficient (-1.17936508).
Square it (1.390901992) and add it to both sides.

Add '1.390901992' to each side of the equation.
-2.358730159x + 1.390901992 + x2 = 30.15873016 + 1.390901992

Reorder the terms:
1.390901992 + -2.358730159x + x2 = 30.15873016 + 1.390901992

Combine like terms: 30.15873016 + 1.390901992 = 31.549632152
1.390901992 + -2.358730159x + x2 = 31.549632152

Factor a perfect square on the left side:
(x + -1.17936508)(x + -1.17936508) = 31.549632152

Calculate the square root of the right side: 5.616905923

Break this problem into two subproblems by setting 
(x + -1.17936508) equal to 5.616905923 and -5.616905923.


Subproblem 1
x + -1.17936508 = 5.616905923

Simplifying
x + -1.17936508 = 5.616905923

Reorder the terms:
-1.17936508 + x = 5.616905923

Solving
-1.17936508 + x = 5.616905923

Solving for variable 'x'.

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

Add '1.17936508' to each side of the equation.
-1.17936508 + 1.17936508 + x = 5.616905923 + 1.17936508

Combine like terms: -1.17936508 + 1.17936508 = 0.00000000
0.00000000 + x = 5.616905923 + 1.17936508
x = 5.616905923 + 1.17936508

Combine like terms: 5.616905923 + 1.17936508 = 6.796271003
x = 6.796271003

Simplifying
x = 6.796271003


Subproblem 2
x + -1.17936508 = -5.616905923

Simplifying
x + -1.17936508 = -5.616905923

Reorder the terms:
-1.17936508 + x = -5.616905923

Solving
-1.17936508 + x = -5.616905923

Solving for variable 'x'.

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

Add '1.17936508' to each side of the equation.
-1.17936508 + 1.17936508 + x = -5.616905923 + 1.17936508

Combine like terms: -1.17936508 + 1.17936508 = 0.00000000
0.00000000 + x = -5.616905923 + 1.17936508
x = -5.616905923 + 1.17936508

Combine like terms: -5.616905923 + 1.17936508 = -4.437540843
x = -4.437540843

Simplifying
x = -4.437540843


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.796271003, -4.437540843}

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