.75x^2+9.72x-200=0

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Solution for .75x^2+9.72x-200=0 equation: 


Simplifying
0.75x2 + 9.72x + -200 = 0

Reorder the terms:
-200 + 9.72x + 0.75x2 = 0

Solving
-200 + 9.72x + 0.75x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.75'.
-266.6666667 + 12.96x + x2 = 0

Move the constant term to the right:

Add '266.6666667' to each side of the equation.
-266.6666667 + 12.96x + 266.6666667 + x2 = 0 + 266.6666667

Reorder the terms:
-266.6666667 + 266.6666667 + 12.96x + x2 = 0 + 266.6666667

Combine like terms: -266.6666667 + 266.6666667 = 0.0000000
0.0000000 + 12.96x + x2 = 0 + 266.6666667
12.96x + x2 = 0 + 266.6666667

Combine like terms: 0 + 266.6666667 = 266.6666667
12.96x + x2 = 266.6666667

The x term is 12.96x.  Take half its coefficient (6.48).
Square it (41.9904) and add it to both sides.

Add '41.9904' to each side of the equation.
12.96x + 41.9904 + x2 = 266.6666667 + 41.9904

Reorder the terms:
41.9904 + 12.96x + x2 = 266.6666667 + 41.9904

Combine like terms: 266.6666667 + 41.9904 = 308.6570667
41.9904 + 12.96x + x2 = 308.6570667

Factor a perfect square on the left side:
(x + 6.48)(x + 6.48) = 308.6570667

Calculate the square root of the right side: 17.568638726

Break this problem into two subproblems by setting 
(x + 6.48) equal to 17.568638726 and -17.568638726.


Subproblem 1
x + 6.48 = 17.568638726

Simplifying
x + 6.48 = 17.568638726

Reorder the terms:
6.48 + x = 17.568638726

Solving
6.48 + x = 17.568638726

Solving for variable 'x'.

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

Add '-6.48' to each side of the equation.
6.48 + -6.48 + x = 17.568638726 + -6.48

Combine like terms: 6.48 + -6.48 = 0.00
0.00 + x = 17.568638726 + -6.48
x = 17.568638726 + -6.48

Combine like terms: 17.568638726 + -6.48 = 11.088638726
x = 11.088638726

Simplifying
x = 11.088638726


Subproblem 2
x + 6.48 = -17.568638726

Simplifying
x + 6.48 = -17.568638726

Reorder the terms:
6.48 + x = -17.568638726

Solving
6.48 + x = -17.568638726

Solving for variable 'x'.

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

Add '-6.48' to each side of the equation.
6.48 + -6.48 + x = -17.568638726 + -6.48

Combine like terms: 6.48 + -6.48 = 0.00
0.00 + x = -17.568638726 + -6.48
x = -17.568638726 + -6.48

Combine like terms: -17.568638726 + -6.48 = -24.048638726
x = -24.048638726

Simplifying
x = -24.048638726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.088638726, -24.048638726}

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