## How to solve an Equation II

# Theory of Equations of First Degree

*This theory about Equations is the continue of the previous post “How to solve an equation”*

**Theory of Biquadrate Equations.**

To solve a biquadrate equation follow these steps:

- If there are parentheses and/or brackets, they are resolved with the necessary operation.

- If there are denominators, it is estimated the m.c.m. and we reduce all fractions to this common denominator.

- Denominators are removed once reduced all terms to m.c.m.

- Each term is simplifies the most possible.

- All terms are left on a member and it is equals to zero.

- The unknown “x²” is replaced by “t” thereby obtaining a quadratic equation.

- The quadratic equation is solved.

- It is performed again replacing, “t” by “x²”, and the square root is performed to obtains the values of “x”.

Example:

# Theory of Equation of degree greater than two.

To solve a degree equation greater than two, not being biquadratic, we apply the Ruffini method as it is explained in Polynomials theory.

In case of grade 3 or higher and, having no independent term, we have to extract common factor “x” and resolve it as it is seen in the example.

Example:

# Theory of notables identities.

Squared binomial:

Examples:

Sum by difference:

Example:

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