What are the solutions to the equation r^2-12sqrt(3)r+80=0 ?

The solutions to the equation r^2-12sqrt(3)r+80=0 are r=2(3sqrt(3)+sqrt(7)),r=2(3sqrt(3)-sqrt(7))

Find the zeros of r^2-12sqrt(3)r+80=0

The zeros of r^2-12sqrt(3)r+80=0 are r=2(3sqrt(3)+sqrt(7)),r=2(3sqrt(3)-sqrt(7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

r^{2} - 123 r + 80 = 0

r = 2 (33 + 7), r = 2 (33 - 7)

Decimal Notation

r = 15.68380 \dots, r = 5.10080 \dots

Solution steps

r^{2} - 123 r + 80 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 12 3 ) \pm ( - 12 3 ) ^{2} - 4 \cdot 1 \cdot 80}{2 \cdot 1}

(- 123)^{2} - 4 \cdot 1 \cdot 80 = 47

r_{1, 2} = \frac{- ( - 12 3 ) \pm 4 7}{2 \cdot 1}

Separate the solutions

r_{1} = \frac{- ( - 12 3 ) + 4 7}{2 \cdot 1}, r_{2} = \frac{- ( - 12 3 ) - 4 7}{2 \cdot 1}

r = \frac{- ( - 12 3 ) + 4 7}{2 \cdot 1} : 2 (33 + 7)

r = \frac{- ( - 12 3 ) - 4 7}{2 \cdot 1} : 2 (33 - 7)

The solutions to the quadratic equation are:

r = 2 (33 + 7), r = 2 (33 - 7)

0 = x^{2} + 12 x + 20

\frac{1}{2} x + 2 = \frac{1}{4} x^{2}

2 x^{2} - 14 x + 10 = 26

5 r^{2} + 215 r + 3 = 0

x^{2} + 4 x = 252

What are the solutions to the equation r^2-12sqrt(3)r+80=0 ?
The solutions to the equation r^2-12sqrt(3)r+80=0 are r=2(3sqrt(3)+sqrt(7)),r=2(3sqrt(3)-sqrt(7))
Find the zeros of r^2-12sqrt(3)r+80=0
The zeros of r^2-12sqrt(3)r+80=0 are r=2(3sqrt(3)+sqrt(7)),r=2(3sqrt(3)-sqrt(7))