how would you factor to make a perfect sqare

label Algebra
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(x^4)+(7x^2)+64

May 18th, 2015

Simplifying
(x4) + (7x2) + 64 = 0
x4 + (7x2) + 64 = 0

Reorder the terms:
64 + (7x2) + x4 = 0

Solving
64 + (7x2) + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + (7x2) + -64 + x4 = 0 + -64

Reorder the terms:
64 + -64 + (7x2) + x4 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + (7x2) + x4 = 0 + -64
(7x2) + x4 = 0 + -64

Combine like terms: 0 + -64 = -64
(7x2) + x4 = -64

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 = -64 + 12.25

Reorder the terms:
12.25 + (7x2) + x4 = -64 + 12.25

Combine like terms: -64 + 12.25 = -51.75
12.25 + (7x2) + x4 = -51.75

Factor a perfect square on the left side:
(x2 + 3.5)(x2 + 3.5) = -51.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

May 18th, 2015

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