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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 49
Capitolo 2, Problema 49

Solve each equation in Exercises 47–64 by completing the square. x2−2x=2x^2 - 2x = 2

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Start with the given quadratic equation: \(x^2 - 2x = 2\).
To complete the square, first move the constant term to the right side (if it's not already isolated): \(x^2 - 2x = 2\) (already isolated in this case).
Take half of the coefficient of \(x\), which is \(-2\), divide by 2 to get \(-1\), then square it to get \((-1)^2 = 1\).
Add this square (1) to both sides of the equation to maintain equality: \(x^2 - 2x + 1 = 2 + 1\).
Rewrite the left side as a perfect square trinomial: \((x - 1)^2 = 3\).

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Completing the Square

Completing the square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. This involves adding a specific value to both sides of the equation to create a binomial squared, making it easier to solve for the variable.
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Solving Quadratic Equations by Completing the Square

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0. Understanding its structure is essential because methods like completing the square rely on manipulating the equation to isolate the variable and find its roots.
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Introduction to Quadratic Equations

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable term stands alone on one side. This step is crucial before completing the square, as it allows you to clearly add the necessary constant to both sides and solve for the variable.
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Equations with Two Variables
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