Write the Word or Phrase That Best Completes Each Statement $\left( 4 x ^ { 2 } + 1 \right) ^ { 2 } + 4 \left( 4 x ^ { 2 } + 1 \right) + 4 = 0 .$

question 52

Short Answer

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Consider the equation $\left( 4 x ^ { 2 } + 1 \right) ^ { 2 } + 4 \left( 4 x ^ { 2 } + 1 \right) + 4 = 0 .$ 4 = 0. If the substitution
u = ________is made, then the equation becomes $u ^ { 2 } + 4 u + 4 = 0$

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Definitions:

Metaphysical Viewpoint

A perspective that deals with questions of existence, the nature and structure of the universe, reality, and the theory of knowledge.

Teleological Metaphysics

The branch of metaphysics that deals with the study of purpose, design, and goals within the universe, often involving the idea that natural processes aim towards certain ends.

Mechanistic Metaphysics

A philosophical viewpoint that regards natural processes as mechanically determined and capable of explanation by laws of physics and chemistry.

Non-teleological

Pertaining to theories or viewpoints that reject the existence of ultimate purposes or ends in natural phenomena or human activities.