step 1 So solve this equation, let's rewrite these negative exponents as rational expressions. So this

X^-2+2 x^-1+1=0 | Numerade

Name: Problem 111, Chapter 7: Elementary and Intermediate Algebra
Uploaded: 2020-04-04T05:13:40-08:00
Duration: 1 min 17 s
Channel: Angela Guo
Description: x^-2+2 x^-1+1=0

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Key Concepts

Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically expressed in the form ax² + bx + c = 0. They can be solved using various methods including factoring, completing the square, or applying the quadratic formula, making them a central topic in algebra.

Algebraic Manipulation

Algebraic manipulation involves the systematic application of algebraic rules to rearrange and simplify expressions. This includes applying exponent rules, factoring, and combining like terms to transform equations into forms that are easier to solve.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. Understanding that x^(-n) equals 1/x^(n) is fundamental for rewriting and simplifying expressions within algebra.

Substitution Method

The substitution method is a strategy used to simplify complex equations by replacing a compound or repeated expression with a single variable. This approach can transform an equation into a more familiar or manageable form, such as converting it into a quadratic equation.

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