Factor the trinomial

x^2-9x+4x

Step-by-step explanation:

Simplifying

x2 + -9x = 4x + -4

Reorder the terms:

-9x + x2 = 4x + -4

Reorder the terms:

-9x + x2 = -4 + 4x

Solving

-9x + x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:

4 + -9x + -4x + x2 = -4 + 4x + 4 + -4x

Combine like terms: -9x + -4x = -13x

4 + -13x + x2 = -4 + 4x + 4 + -4x

Reorder the terms:

4 + -13x + x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0

4 + -13x + x2 = 0 + 4x + -4x

4 + -13x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0

4 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.

4 + -13x + -4 + x2 = 0 + -4

Reorder the terms:

4 + -4 + -13x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0

0 + -13x + x2 = 0 + -4

-13x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4

-13x + x2 = -4

The x term is -13x.  Take half its coefficient (-6.5).

Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.

-13x + 42.25 + x2 = -4 + 42.25

Reorder the terms:

42.25 + -13x + x2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25

42.25 + -13x + x2 = 38.25

Factor a perfect square on the left side:

(x + -6.5)(x + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting  

(x + -6.5) equal to 6.184658438 and -6.184658438.

Step-by-step explanation:Simplifying

x2 + -9x = 4x + -4

Reorder the terms:

-9x + x2 = 4x + -4

Reorder the terms:

-9x + x2 = -4 + 4x

Solving

-9x + x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:

4 + -9x + -4x + x2 = -4 + 4x + 4 + -4x

Combine like terms: -9x + -4x = -13x

4 + -13x + x2 = -4 + 4x + 4 + -4x

Reorder the terms:

4 + -13x + x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0

4 + -13x + x2 = 0 + 4x + -4x

4 + -13x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0

4 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.

4 + -13x + -4 + x2 = 0 + -4

Reorder the terms:

4 + -4 + -13x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0

0 + -13x + x2 = 0 + -4

-13x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4

-13x + x2 = -4

The x term is -13x.  Take half its coefficient (-6.5).

Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.

-13x + 42.25 + x2 = -4 + 42.25

Reorder the terms:

42.25 + -13x + x2 = -4 + 42.25

Combine like terms: -4 + 42.25 = 38.25

42.25 + -13x + x2 = 38.25

Factor a perfect square on the left side:

(x + -6.5)(x + -6.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting  

(x + -6.5) equal to 6.184658438 and -6.184658438.