Solve each equation in Exercises 15–34 by the square root property. 3x² - 1 = 47

검증된 단계별 안내

Start by isolating the quadratic term. Add 1 to both sides of the equation to eliminate the constant term on the left-hand side:

3x^2 = 47 + 1

Simplify the right-hand side to combine the constants:

3x^2 = 48

Divide both sides of the equation by 3 to isolate

x^2

x^2 = \(\frac{48}{3}\)

Simplify the fraction on the right-hand side:

x^2 = 16

Apply the square root property to solve for

x

. Remember to include both the positive and negative roots:

x = \(\pm\) \(\sqrt{16}\)

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

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Square Root Property

The square root property states that if an equation is in the form of x^2 = k, then the solutions for x can be found by taking the square root of both sides, resulting in x = ±√k. This property is essential for solving quadratic equations where the variable is squared.

Rearranging Equations

Rearranging equations involves manipulating the equation to isolate the variable of interest. In the context of the given equation, this means moving all terms to one side to set the equation to zero or isolating the squared term to apply the square root property effectively.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. Understanding the standard form of quadratic equations is crucial for applying various solving techniques, including the square root property, factoring, and the quadratic formula.

Solve each equation in Exercises 15–34 by the square root property. 3x2 - 1 = 47