9x^2-103x+288=

Solution for 9x^2-103x+288= equation:

Simplifying
9x2 + -103x + 288 = 0

Reorder the terms:
288 + -103x + 9x2 = 0

Solving
288 + -103x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
32 + -11.44444444x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -11.44444444x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -11.44444444x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -11.44444444x + x2 = 0 + -32
-11.44444444x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-11.44444444x + x2 = -32

The x term is -11.44444444x.  Take half its coefficient (-5.72222222).
Square it (32.74382714) and add it to both sides.

Add '32.74382714' to each side of the equation.
-11.44444444x + 32.74382714 + x2 = -32 + 32.74382714

Reorder the terms:
32.74382714 + -11.44444444x + x2 = -32 + 32.74382714

Combine like terms: -32 + 32.74382714 = 0.74382714
32.74382714 + -11.44444444x + x2 = 0.74382714

Factor a perfect square on the left side:
(x + -5.72222222)(x + -5.72222222) = 0.74382714

Calculate the square root of the right side: 0.862454138

Break this problem into two subproblems by setting 
(x + -5.72222222) equal to 0.862454138 and -0.862454138.

Subproblem 1
x + -5.72222222 = 0.862454138

Simplifying
x + -5.72222222 = 0.862454138

Reorder the terms:
-5.72222222 + x = 0.862454138

Solving
-5.72222222 + x = 0.862454138

Solving for variable 'x'.

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

Add '5.72222222' to each side of the equation.
-5.72222222 + 5.72222222 + x = 0.862454138 + 5.72222222

Combine like terms: -5.72222222 + 5.72222222 = 0.00000000
0.00000000 + x = 0.862454138 + 5.72222222
x = 0.862454138 + 5.72222222

Combine like terms: 0.862454138 + 5.72222222 = 6.584676358
x = 6.584676358

Simplifying
x = 6.584676358

Subproblem 2
x + -5.72222222 = -0.862454138

Simplifying
x + -5.72222222 = -0.862454138

Reorder the terms:
-5.72222222 + x = -0.862454138

Solving
-5.72222222 + x = -0.862454138

Solving for variable 'x'.

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

Add '5.72222222' to each side of the equation.
-5.72222222 + 5.72222222 + x = -0.862454138 + 5.72222222

Combine like terms: -5.72222222 + 5.72222222 = 0.00000000
0.00000000 + x = -0.862454138 + 5.72222222
x = -0.862454138 + 5.72222222

Combine like terms: -0.862454138 + 5.72222222 = 4.859768082
x = 4.859768082

Simplifying
x = 4.859768082

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.584676358, 4.859768082}