-3x(x-10)=33

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Solution for -3x(x-10)=33 equation: 


Simplifying
-3x(x + -10) = 33

Reorder the terms:
-3x(-10 + x) = 33
(-10 * -3x + x * -3x) = 33
(30x + -3x2) = 33

Solving
30x + -3x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 30x + -3x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 10x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
-11 + 10x + -1x2 = 0

Solving
-11 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
11 + -10x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -10x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -10x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -10x + x2 = 0 + -11
-10x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-10x + x2 = -11

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -11 + 25

Reorder the terms:
25 + -10x + x2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + -10x + x2 = 14

Factor a perfect square on the left side:
(x + -5)(x + -5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -5) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -5 = 3.741657387

Simplifying
x + -5 = 3.741657387

Reorder the terms:
-5 + x = 3.741657387

Solving
-5 + x = 3.741657387

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.741657387 + 5
x = 3.741657387 + 5

Combine like terms: 3.741657387 + 5 = 8.741657387
x = 8.741657387

Simplifying
x = 8.741657387


Subproblem 2
x + -5 = -3.741657387

Simplifying
x + -5 = -3.741657387

Reorder the terms:
-5 + x = -3.741657387

Solving
-5 + x = -3.741657387

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.741657387 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.741657387 + 5
x = -3.741657387 + 5

Combine like terms: -3.741657387 + 5 = 1.258342613
x = 1.258342613

Simplifying
x = 1.258342613


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.741657387, 1.258342613}
Solution
x = {8.741657387, 1.258342613}

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