Solve each quadratic equation using the square root property. See Example 6. x² = 16

검증된 단계별 안내

Identify the given quadratic equation: \(x^{2} = 16\).

Recall the square root property, which states that if \(x^{2} = k\), then \(x = \pm \sqrt{k}\).

Apply the square root property to the equation: \(x = \pm \sqrt{16}\).

Simplify the square root: \(x = \pm 4\).

Write the final solution as two values: \(x = 4\) and \(x = -4\).

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주요 개념

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

Square Root Property

The square root property states that if x² = k, then x = ±√k. This means to solve an equation where a variable is squared and set equal to a number, you take the square root of both sides, considering both positive and negative roots.

Solving Quadratic Equations

Quadratic equations are polynomial equations of degree two, often written as ax² + bx + c = 0. When the equation is in the form x² = k, it can be solved directly using the square root property without factoring or using the quadratic formula.

Simplifying Square Roots

When taking the square root of a number, it is important to simplify the radical if possible. For example, √16 simplifies to 4. Simplifying helps in finding exact solutions and understanding the nature of the roots.