Question

Factor
x² - 38x+ 361=0​

Answer 1

Answer:

x + 19

Step-by-step explanation:

Simplifying

x2 + 38x + -361 = 0

Reorder the terms:

-361 + 38x + x2 = 0

Solving

-361 + 38x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '361' to each side of the equation.

-361 + 38x + 361 + x2 = 0 + 361

Reorder the terms:

-361 + 361 + 38x + x2 = 0 + 361

Combine like terms: -361 + 361 = 0

0 + 38x + x2 = 0 + 361

38x + x2 = 0 + 361

Combine like terms: 0 + 361 = 361

38x + x2 = 361

The x term is 38x.  Take half its coefficient (19).

Square it (361) and add it to both sides.

Add '361' to each side of the equation.

38x + 361 + x2 = 361 + 361

Reorder the terms:

361 + 38x + x2 = 361 + 361

Combine like terms: 361 + 361 = 722

361 + 38x + x2 = 722

Factor a perfect square on the left side:

(x + 19)(x + 19) = 722

Answer 2

${x}^{2} - 19x - 19x + 361$

$x(x - 19) - 19(x - 19)$

$x - 19 = 0$

$x = 19$

Checking

${x}^{2} - 38x + 361 = 0$

we know that. x = 19

putting the value

${19}^{2} - 38(19) + 361 = 0$

$361 - 38(19) + 361 = 0$

$361 - 722 + 361 = 0$

$(361 + 361) - 722 = 0$

$722 - 722 = 0$

$0 = 0$

factor of given equation is 19