Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

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Start with the given quadratic equation: \(y^2 - 6y - 4 = 0\).

Move the constant term to the right side to isolate the terms involving \(y\): \(y^2 - 6y = 4\).

To complete the square, take half of the coefficient of \(y\) (which is \(-6\)), divide by 2 to get \(-3\), then square it to get \((-3)^2 = 9\).

Add 9 to both sides of the equation to maintain equality: \(y^2 - 6y + 9 = 4 + 9\).

Rewrite the left side as a perfect square trinomial: \((y - 3)^2 = 13\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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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 and subtracting a specific value 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 for applying methods like completing the square, factoring, or using the quadratic formula to find the 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 simplifies the process and helps in accurately solving the equation.