What are the solutions to the equation (3x-1)^2=x^2+21 ?

The solutions to the equation (3x-1)^2=x^2+21 are x=2,x=-5/4

Find the zeros of (3x-1)^2=x^2+21

The zeros of (3x-1)^2=x^2+21 are x=2,x=-5/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(3 x - 1)^{2} = x^{2} + 21

x = 2, x = - \frac{5}{4}

Decimal Notation

x = 2, x = - 1.25

Solution steps

(3 x - 1)^{2} = x^{2} + 21

Expand

(3 x - 1)^{2} : 9 x^{2} - 6 x + 1

9 x^{2} - 6 x + 1 = x^{2} + 21

Move

21

to the left side

9 x^{2} - 6 x - 20 = x^{2}

Move

x^{2}

to the left side

8 x^{2} - 6 x - 20 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 8 ( - 20 )}{2 \cdot 8}

(- 6)^{2} - 4 \cdot 8 (- 20) = 26

x_{1, 2} = \frac{- ( - 6 ) \pm 26}{2 \cdot 8}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 26}{2 \cdot 8}, x_{2} = \frac{- ( - 6 ) - 26}{2 \cdot 8}

x = \frac{- ( - 6 ) + 26}{2 \cdot 8} : 2

x = \frac{- ( - 6 ) - 26}{2 \cdot 8} : - \frac{5}{4}

The solutions to the quadratic equation are:

x = 2, x = - \frac{5}{4}

x^{2} = - x^{2} + 2 x + 4

x^{2} - 40 x + 256 = 0

k^{2} - 6 k + 1 = 0

x, x^{2} - 3 x + 4 = 0

x^{2} - 4 x + 3.5 = 0

What are the solutions to the equation (3x-1)^2=x^2+21 ?
The solutions to the equation (3x-1)^2=x^2+21 are x=2,x=-5/4
Find the zeros of (3x-1)^2=x^2+21
The zeros of (3x-1)^2=x^2+21 are x=2,x=-5/4