Question

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

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

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 5, Problem 31

Instant Answer

Solved by Expert Ankit Gupta

03/17/2020

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Solve each 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 typically written as ax² + bx + c = 0. It represents a fundamental type of equation in algebra that models parabolic relationships and appears across various mathematical and practical applications.

Standard Form

The standard form of a quadratic equation, ax² + bx + c = 0, provides a uniform way to represent quadratic equations. This formulation is crucial because it enables the application of various methods, such as factoring, completing the square, or the quadratic formula, to find solutions.

Completing the Square

Completing the square is a method used to solve quadratic equations by rewriting the quadratic expression as a perfect square trinomial. By adding and subtracting the appropriate constant term, the equation is transformed into a form that allows isolation of the squared term, leading to straightforward extraction of the variable's value through the square root operation.

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