Solve each equation in Exercises 83–108 by the method of your choice. $9 - 6 x + x^{2} = 0$

검증된 단계별 안내

Rewrite the quadratic equation in standard form: $x^2 - 6x + 9 = 0$.

Identify the coefficients: $a = 1$, $b = -6$, and $c = 9$.

Calculate the discriminant using the formula $\Delta = b^2 - 4ac$ to determine the nature of the roots.

Apply the quadratic formula $x = \frac{-b \pm \sqrt{\Delta}}{2a}$ to find the solutions for $x$.

Simplify the expression under the square root and then simplify the entire expression to write the solutions in simplest form.

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주요 개념

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

Quadratic Equations

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0. It typically has two solutions, which can be real or complex numbers. Understanding the structure of quadratic equations is essential for solving them effectively.

Factoring Quadratic Expressions

Factoring involves rewriting a quadratic expression as a product of two binomials. This method is useful when the quadratic can be easily factored, allowing you to set each factor equal to zero to find the solutions. It simplifies solving quadratics without using formulas.

Quadratic Formula

The quadratic formula x = (-b ± √(b² - 4ac)) / (2a) provides a universal method to solve any quadratic equation. It uses the coefficients a, b, and c to find the roots, including complex solutions when the discriminant (b² - 4ac) is negative.

Solve each equation in Exercises 83–108 by the method of your choice. 9−6x+x2=09 - 6x + x^2 = 0