3x(x-53)=84

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Solution for 3x(x-53)=84 equation: 


Simplifying
3x(x + -53) = 84

Reorder the terms:
3x(-53 + x) = 84
(-53 * 3x + x * 3x) = 84
(-159x + 3x2) = 84

Solving
-159x + 3x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -159x + 3x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -159x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -53x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-28 + -53x + x2)' equal to zero and attempt to solve:

Simplifying
-28 + -53x + x2 = 0

Solving
-28 + -53x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -53x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -53x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -53x + x2 = 0 + 28
-53x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-53x + x2 = 28

The x term is -53x.  Take half its coefficient (-26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
-53x + 702.25 + x2 = 28 + 702.25

Reorder the terms:
702.25 + -53x + x2 = 28 + 702.25

Combine like terms: 28 + 702.25 = 730.25
702.25 + -53x + x2 = 730.25

Factor a perfect square on the left side:
(x + -26.5)(x + -26.5) = 730.25

Calculate the square root of the right side: 27.023138234

Break this problem into two subproblems by setting 
(x + -26.5) equal to 27.023138234 and -27.023138234.


Subproblem 1
x + -26.5 = 27.023138234

Simplifying
x + -26.5 = 27.023138234

Reorder the terms:
-26.5 + x = 27.023138234

Solving
-26.5 + x = 27.023138234

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = 27.023138234 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = 27.023138234 + 26.5
x = 27.023138234 + 26.5

Combine like terms: 27.023138234 + 26.5 = 53.523138234
x = 53.523138234

Simplifying
x = 53.523138234


Subproblem 2
x + -26.5 = -27.023138234

Simplifying
x + -26.5 = -27.023138234

Reorder the terms:
-26.5 + x = -27.023138234

Solving
-26.5 + x = -27.023138234

Solving for variable 'x'.

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

Add '26.5' to each side of the equation.
-26.5 + 26.5 + x = -27.023138234 + 26.5

Combine like terms: -26.5 + 26.5 = 0.0
0.0 + x = -27.023138234 + 26.5
x = -27.023138234 + 26.5

Combine like terms: -27.023138234 + 26.5 = -0.523138234
x = -0.523138234

Simplifying
x = -0.523138234


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.523138234, -0.523138234}
Solution
x = {53.523138234, -0.523138234}

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