(x-3)(x+4)=0.33

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Solution for (x-3)(x+4)=0.33 equation: 


Simplifying
(x + -3)(x + 4) = 0.33

Reorder the terms:
(-3 + x)(x + 4) = 0.33

Reorder the terms:
(-3 + x)(4 + x) = 0.33

Multiply (-3 + x) * (4 + x)
(-3(4 + x) + x(4 + x)) = 0.33
((4 * -3 + x * -3) + x(4 + x)) = 0.33
((-12 + -3x) + x(4 + x)) = 0.33
(-12 + -3x + (4 * x + x * x)) = 0.33
(-12 + -3x + (4x + x2)) = 0.33

Combine like terms: -3x + 4x = 1x
(-12 + 1x + x2) = 0.33

Solving
-12 + 1x + x2 = 0.33

Solving for variable 'x'.

Reorder the terms:
-12 + -0.33 + 1x + x2 = 0.33 + -0.33

Combine like terms: -12 + -0.33 = -12.33
-12.33 + 1x + x2 = 0.33 + -0.33

Combine like terms: 0.33 + -0.33 = 0.00
-12.33 + 1x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '12.33' to each side of the equation.
-12.33 + 1x + 12.33 + x2 = 0.00 + 12.33

Reorder the terms:
-12.33 + 12.33 + 1x + x2 = 0.00 + 12.33

Combine like terms: -12.33 + 12.33 = 0.00
0.00 + 1x + x2 = 0.00 + 12.33
1x + x2 = 0.00 + 12.33

Combine like terms: 0.00 + 12.33 = 12.33
1x + x2 = 12.33

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 12.33 + 0.25

Reorder the terms:
0.25 + x + x2 = 12.33 + 0.25

Combine like terms: 12.33 + 0.25 = 12.58
0.25 + x + x2 = 12.58

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 12.58

Calculate the square root of the right side: 3.54682957

Break this problem into two subproblems by setting 
(x + 0.5) equal to 3.54682957 and -3.54682957.


Subproblem 1
x + 0.5 = 3.54682957

Simplifying
x + 0.5 = 3.54682957

Reorder the terms:
0.5 + x = 3.54682957

Solving
0.5 + x = 3.54682957

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 3.54682957 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 3.54682957 + -0.5
x = 3.54682957 + -0.5

Combine like terms: 3.54682957 + -0.5 = 3.04682957
x = 3.04682957

Simplifying
x = 3.04682957


Subproblem 2
x + 0.5 = -3.54682957

Simplifying
x + 0.5 = -3.54682957

Reorder the terms:
0.5 + x = -3.54682957

Solving
0.5 + x = -3.54682957

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -3.54682957 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -3.54682957 + -0.5
x = -3.54682957 + -0.5

Combine like terms: -3.54682957 + -0.5 = -4.04682957
x = -4.04682957

Simplifying
x = -4.04682957


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.04682957, -4.04682957}

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