Question

factorise .........x^4 +7x^2 +16

Answer 1

Simplifying
x4 + -7x2 + 16 = 0

Reorder the terms:
16 + -7x2 + x4 = 0

Solving
16 + -7x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -7x2 + -16 + x4 = 0 + -16

Reorder the terms:
16 + -16 + -7x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -7x2 + x4 = 0 + -16
-7x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16
-7x2 + x4 = -16

The x term is -7x2. Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x2 + 12.25 + x4 = -16 + 12.25

Reorder the terms:
12.25 + -7x2 + x4 = -16 + 12.25

Combine like terms: -16 + 12.25 = -3.75
12.25 + -7x2 + x4 = -3.75

Factor a perfect square on the left side:
(x2 + -3.5)(x2 + -3.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

Answer 2

Answer:

Step-by-step explanation:

Simplifying

x4 + -7x2 + 16 = 0

Reorder the terms:

16 + -7x2 + x4 = 0

Solving

16 + -7x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.

16 + -7x2 + -16 + x4 = 0 + -16

Reorder the terms:

16 + -16 + -7x2 + x4 = 0 + -16

Combine like terms: 16 + -16 = 0

0 + -7x2 + x4 = 0 + -16

-7x2 + x4 = 0 + -16

Combine like terms: 0 + -16 = -16

-7x2 + x4 = -16

The x term is -7x2. Take half its coefficient (-3.5).

Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.

-7x2 + 12.25 + x4 = -16 + 12.25

Reorder the terms:

12.25 + -7x2 + x4 = -16 + 12.25

Combine like terms: -16 + 12.25 = -3.75

12.25 + -7x2 + x4 = -3.75

Factor a perfect square on the left side:

(x2 + -3.5)(x2 + -3.5) = -3.75