(X+X-3)X=36

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Solution for (X+X-3)X=36 equation:


Simplifying
(X + X + -3) * X = 36

Reorder the terms:
(-3 + X + X) * X = 36

Combine like terms: X + X = 2X
(-3 + 2X) * X = 36

Reorder the terms for easier multiplication:
X(-3 + 2X) = 36
(-3 * X + 2X * X) = 36
(-3X + 2X2) = 36

Solving
-3X + 2X2 = 36

Solving for variable 'X'.

Reorder the terms:
-36 + -3X + 2X2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -3X + 2X2 = 0

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

Divide each side by '2'.
-18 + -1.5X + X2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1.5X + 18 + X2 = 0 + 18

Reorder the terms:
-18 + 18 + -1.5X + X2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1.5X + X2 = 0 + 18
-1.5X + X2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1.5X + X2 = 18

The X term is -1.5X.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5X + 0.5625 + X2 = 18 + 0.5625

Reorder the terms:
0.5625 + -1.5X + X2 = 18 + 0.5625

Combine like terms: 18 + 0.5625 = 18.5625
0.5625 + -1.5X + X2 = 18.5625

Factor a perfect square on the left side:
(X + -0.75)(X + -0.75) = 18.5625

Calculate the square root of the right side: 4.308421985

Break this problem into two subproblems by setting 
(X + -0.75) equal to 4.308421985 and -4.308421985.

Subproblem 1

X + -0.75 = 4.308421985 Simplifying X + -0.75 = 4.308421985 Reorder the terms: -0.75 + X = 4.308421985 Solving -0.75 + X = 4.308421985 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + X = 4.308421985 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = 4.308421985 + 0.75 X = 4.308421985 + 0.75 Combine like terms: 4.308421985 + 0.75 = 5.058421985 X = 5.058421985 Simplifying X = 5.058421985

Subproblem 2

X + -0.75 = -4.308421985 Simplifying X + -0.75 = -4.308421985 Reorder the terms: -0.75 + X = -4.308421985 Solving -0.75 + X = -4.308421985 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + X = -4.308421985 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + X = -4.308421985 + 0.75 X = -4.308421985 + 0.75 Combine like terms: -4.308421985 + 0.75 = -3.558421985 X = -3.558421985 Simplifying X = -3.558421985

Solution

The solution to the problem is based on the solutions from the subproblems. X = {5.058421985, -3.558421985}

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