3x(x-3)=25

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Solution for 3x(x-3)=25 equation: 


Simplifying
3x(x + -3) = 25

Reorder the terms:
3x(-3 + x) = 25
(-3 * 3x + x * 3x) = 25
(-9x + 3x2) = 25

Solving
-9x + 3x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + -9x + 3x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -9x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + -3x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + -3x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + -3x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + -3x + x2 = 0 + 8.333333333
-3x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
-3x + x2 = 8.333333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 8.333333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 8.333333333 + 2.25

Combine like terms: 8.333333333 + 2.25 = 10.583333333
2.25 + -3x + x2 = 10.583333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 10.583333333

Calculate the square root of the right side: 3.253203549

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.253203549 and -3.253203549.


Subproblem 1
x + -1.5 = 3.253203549

Simplifying
x + -1.5 = 3.253203549

Reorder the terms:
-1.5 + x = 3.253203549

Solving
-1.5 + x = 3.253203549

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 3.253203549 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 3.253203549 + 1.5
x = 3.253203549 + 1.5

Combine like terms: 3.253203549 + 1.5 = 4.753203549
x = 4.753203549

Simplifying
x = 4.753203549


Subproblem 2
x + -1.5 = -3.253203549

Simplifying
x + -1.5 = -3.253203549

Reorder the terms:
-1.5 + x = -3.253203549

Solving
-1.5 + x = -3.253203549

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -3.253203549 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -3.253203549 + 1.5
x = -3.253203549 + 1.5

Combine like terms: -3.253203549 + 1.5 = -1.753203549
x = -1.753203549

Simplifying
x = -1.753203549


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.753203549, -1.753203549}

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