Question

Explain why the equation $(x+2)^{2}+5=1$ has no real number solutions.

Name: Problem 84, Chapter 6: Intermediate Algebra
Uploaded: 2022-03-01T22:21:11-08:00
Duration: 25 s
Channel: James Kiss
Description: Explain why the equation (x+2)^2+5=1 has no real number solutions.

   Explain why the equation $(x+2)^{2}+5=1$ has no real number solutions.

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 6, Problem 84

Instant Answer

Solved by Expert James Kiss

03/01/2022

Step 1

This gives us: $$(x+2)^{2}+5-5=1-5$$ which simplifies to: $$(x+2)^{2}=-4$$ Show more…

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Explain why the equation $(x+2)^{2}+5=1$ has no real number solutions.

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Key Concepts

Non-negativity of Squared Real Numbers

In real numbers, squaring any value always produces a non-negative result. This is because both positive and negative numbers become positive when squared, and zero remains zero. Therefore, an expression like the square of a binomial is never negative for any real input.

Equations with No Real Solutions

When solving equations, if isolating a squared term results in a negative value, it indicates there is no real number that can satisfy the equation. This is due to the fact that no real number, when squared, can yield a negative number, meaning the equation has no solution in the set of real numbers.

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