Solve each equation in Exercises 15–34 by the square root property. $(3 x + 2)^{2} = 9$

검증된 단계별 안내

Identify the equation given: $ (3x + 2)^2 = 9 $. This is a perfect setup for the square root property because the variable expression is squared.

Apply the square root property, which states that if $ A^2 = B $, then $ A = \pm \sqrt{B} $. Here, set $ 3x + 2 = \pm \sqrt{9} $.

Simplify the square root: $ \sqrt{9} = 3 $, so rewrite the equation as $ 3x + 2 = \pm 3 $. This gives two separate equations to solve: $ 3x + 2 = 3 $ and $ 3x + 2 = -3 $.

Solve each linear equation separately. For $ 3x + 2 = 3 $, subtract 2 from both sides to isolate the term with $ x $. For $ 3x + 2 = -3 $, do the same.

Finally, divide both sides of each equation by 3 to solve for $ x $. This will give you the two possible solutions for $ x $.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

Square Root Property

The square root property states that if an equation is in the form (expression)^2 = k, then the solution can be found by taking the square root of both sides, resulting in expression = ±√k. This method is useful for solving quadratic equations that are already isolated as a perfect square.

Isolating the Squared Term

Before applying the square root property, it is essential to isolate the squared term on one side of the equation. This means manipulating the equation so that (3x + 2)^2 stands alone, allowing you to take the square root of both sides accurately.

Solving Linear Equations After Taking Square Roots

After applying the square root property, you get two linear equations due to the ± sign. Solving these linear equations involves isolating the variable x by performing inverse operations such as addition, subtraction, multiplication, or division.

Solve each equation in Exercises 15–34 by the square root property.(3x+2)2=9 (3x + 2)^2 = 9