Exercises 137–139 will help you prepare for the material covered in the next section. Solve: x(x - 7) = 3.

검증된 단계별 안내

Start by expanding the left side of the equation:

x (x - 7) = x \cdot x - x \cdot 7 = x^{2} - 7x

Rewrite the equation with the expanded form:

x^{2} - 7x = 3

Bring all terms to one side to set the equation equal to zero:

x^{2} - 7x - 3 = 0

Identify the coefficients for the quadratic equation in standard form

ax^2 + bx + c = 0

: here,

a = 1

b = -7

, and

c = -3

Use the quadratic formula to solve for

x

x = \(\frac{-b \pm \sqrt{b^2 - 4ac}\)}{2a}

. Substitute the values of

a

b

, and

c

into the formula.

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.

Expanding and Simplifying Algebraic Expressions

This involves applying the distributive property to multiply terms within parentheses and then combining like terms. For example, expanding x(x - 7) results in x² - 7x, which simplifies the equation for easier manipulation.

Solving Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically in the form ax² + bx + c = 0. Solving them can involve factoring, completing the square, or using the quadratic formula to find the values of x that satisfy the equation.

Setting Equations to Zero

To solve quadratic equations, it is essential to rewrite the equation so that one side equals zero. This allows the use of factoring or the quadratic formula by isolating all terms on one side, creating a standard form ax² + bx + c = 0.