Solve. (m^2+7)^2-6(m^2+7)-16=0

Name: Problem 46, Chapter 11: Elementary and Intermediate Algebra
Uploaded: 2020-05-24T02:51:25-08:00
Duration: 1 min 12 s
Channel: Heather Zimmers
Description: Solve. (m^2+7)^2-6(m^2+7)-16=0

step 1 Let's reduce this equation to quadratic form by doing a U substitution. So we can look at the mi

Question

Solve. $$ \left(m^{2}+7\right)^{2}-6\left(m^{2}+7\right)-16=0 $$

   Solve.
$$
\left(m^{2}+7\right)^{2}-6\left(m^{2}+7\right)-16=0
$$

Elementary and Intermediate Algebra

Marvin L. Bittinger,… 4th Edition

Chapter 11, Problem 46

Instant Answer

Solved by Expert Heather Zimmers

05/24/2020

Step 1

The equation then becomes: $$ u^{2}-6u-16=0 $$ Show more…

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Solve. $$ \left(m^{2}+7\right)^{2}-6\left(m^{2}+7\right)-16=0 $$

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Key Concepts

Variable Substitution

This concept involves replacing a complex or repetitive expression with a new variable to simplify an equation. By doing so, you reduce an equation that might initially appear difficult to manage into a more familiar form, often leading to a standard quadratic equation that is easier to solve.

Quadratic Equation

A quadratic equation is a second-degree polynomial equation, typically expressed in the form ax² + bx + c = 0. The process of solving such equations can involve factoring, completing the square, or using the quadratic formula, all of which are fundamental techniques in algebra.

Factoring Techniques

Factoring involves rewriting an equation as a product of simpler expressions, which can then be set to zero to find solutions. This method is particularly useful when an equation is already in a quadratic form, as it can reveal the underlying structure of the roots and simplify the solving process.

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