Solve each equation in Exercises 47–64 by completing the square. $x^{2} - 2 x = 2$

검증된 단계별 안내

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: $(x - 1)^2 = 3$.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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