Question

Solve equation by completing the square. $$ x^{2}+4 x+1=0 $$

   Solve equation by completing the square.
$$
x^{2}+4 x+1=0
$$

Algebra and Trigonometry

Algebra and Trigonometry

Robert Blitzer 6th Edition

Chapter 1, Problem 53

Instant Answer

Solved by Expert James Kiss

12/15/2020

Step 1

Step 1: First, we rewrite the equation $x^{2}+4 x+1=0$ as $x^{2}+4 x=-1$ by subtracting 1 from both sides. Show more…

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Solve equation by completing the square. $$ x^{2}+4 x+1=0 $$

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation in one variable. It is generally written in the form ax² + bx + c = 0, where a, b, and c are constants. This type of equation is fundamental in algebra and has a variety of methods for finding its roots, which are the values of the variable that satisfy the equation.

Completing the Square

Completing the square is a technique used to convert a quadratic equation into a form that features a perfect square trinomial. This method involves manipulating the equation so that one side becomes a perfect square, allowing one to solve for the variable by applying the square root property. It not only serves as an alternative to the quadratic formula but also provides insight into the structure of quadratic expressions and helps in deriving the vertex form of a quadratic function.

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