step 1 Here we have 2m to the 4th power plus 1 is equal to 7m squared. So we're solving for m, and we w

Solve. 2 m^4+1=7 m^2

Name: Problem 59, Chapter 11: Beginning and Intermediate Algebra
Uploaded: 2020-06-27T22:23:16-08:00
Duration: 2 min 52 s
Channel: Ethan Somes
Description: Solve. 2 m^4+1=7 m^2

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Key Concepts

Polynomial Equations

A polynomial equation involves variables raised to whole number exponents, with the equation set equal to a value (typically zero). In this context, the equation 2m? + 1 = 7m² is a quartic equation, meaning the highest exponent is four. Polynomial equations are fundamental in algebra and can often be solved by factoring, substitution, or other algebraic techniques.

Substitution Method

The substitution method is a technique used to simplify equations by replacing a complicated expression with a single variable. In this problem, noticing that m? and m² are powers of m allows us to set x = m², thereby transforming the original quartic equation into a quadratic equation in terms of x. This method simplifies solving the equation significantly.

Quadratic Formula

The quadratic formula is a standard method for solving quadratic equations of the form ax² + bx + c = 0. Once the equation is rewritten in quadratic form using the substitution x = m², the quadratic formula can be applied to find the values of x. After solving for x, the final step involves taking square roots to determine the values of the original variable m.

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