x(x-5)=42

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Solution for x(x-5)=42 equation:


Simplifying
x(x + -5) = 42

Reorder the terms:
x(-5 + x) = 42
(-5 * x + x * x) = 42
(-5x + x2) = 42

Solving
-5x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -5x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -5x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -5x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -5x + x2 = 0 + 42
-5x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-5x + x2 = 42

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 = 42 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 42 + 6.25

Combine like terms: 42 + 6.25 = 48.25
6.25 + -5x + x2 = 48.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -2.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + -2.5 = 6.946221995

Simplifying
x + -2.5 = 6.946221995

Reorder the terms:
-2.5 + x = 6.946221995

Solving
-2.5 + x = 6.946221995

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 = 6.946221995 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 6.946221995 + 2.5
x = 6.946221995 + 2.5

Combine like terms: 6.946221995 + 2.5 = 9.446221995
x = 9.446221995

Simplifying
x = 9.446221995


Subproblem 2
x + -2.5 = -6.946221995

Simplifying
x + -2.5 = -6.946221995

Reorder the terms:
-2.5 + x = -6.946221995

Solving
-2.5 + x = -6.946221995

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 = -6.946221995 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -6.946221995 + 2.5
x = -6.946221995 + 2.5

Combine like terms: -6.946221995 + 2.5 = -4.446221995
x = -4.446221995

Simplifying
x = -4.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.446221995, -4.446221995}

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