x(x-5)=387

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Solution for x(x-5)=387 equation: 


Simplifying
x(x + -5) = 387

Reorder the terms:
x(-5 + x) = 387
(-5 * x + x * x) = 387
(-5x + x2) = 387

Solving
-5x + x2 = 387

Solving for variable 'x'.

Reorder the terms:
-387 + -5x + x2 = 387 + -387

Combine like terms: 387 + -387 = 0
-387 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '387' to each side of the equation.
-387 + -5x + 387 + x2 = 0 + 387

Reorder the terms:
-387 + 387 + -5x + x2 = 0 + 387

Combine like terms: -387 + 387 = 0
0 + -5x + x2 = 0 + 387
-5x + x2 = 0 + 387

Combine like terms: 0 + 387 = 387
-5x + x2 = 387

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 387 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 387 + 6.25

Combine like terms: 387 + 6.25 = 393.25
6.25 + -5x + x2 = 393.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 393.25

Calculate the square root of the right side: 19.830532015

Break this problem into two subproblems by setting 
(x + -2.5) equal to 19.830532015 and -19.830532015.


Subproblem 1
x + -2.5 = 19.830532015

Simplifying
x + -2.5 = 19.830532015

Reorder the terms:
-2.5 + x = 19.830532015

Solving
-2.5 + x = 19.830532015

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 19.830532015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 19.830532015 + 2.5
x = 19.830532015 + 2.5

Combine like terms: 19.830532015 + 2.5 = 22.330532015
x = 22.330532015

Simplifying
x = 22.330532015


Subproblem 2
x + -2.5 = -19.830532015

Simplifying
x + -2.5 = -19.830532015

Reorder the terms:
-2.5 + x = -19.830532015

Solving
-2.5 + x = -19.830532015

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -19.830532015 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -19.830532015 + 2.5
x = -19.830532015 + 2.5

Combine like terms: -19.830532015 + 2.5 = -17.330532015
x = -17.330532015

Simplifying
x = -17.330532015


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.330532015, -17.330532015}

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