What are the solutions to the equation r^2-6r+19=6r ?

The solutions to the equation r^2-6r+19=6r are r=6+sqrt(17),r=6-sqrt(17)

Find the zeros of r^2-6r+19=6r

The zeros of r^2-6r+19=6r are r=6+sqrt(17),r=6-sqrt(17)

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r^{2} - 6 r + 19 = 6 r

r = 6 + 17, r = 6 - 17

Decimal Notation

r = 10.12310 \dots, r = 1.87689 \dots

Solution steps

r^{2} - 6 r + 19 = 6 r

Move

6 r

to the left side

r^{2} - 12 r + 19 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 1 \cdot 19}{2 \cdot 1}

(- 12)^{2} - 4 \cdot 1 \cdot 19 = 217

r_{1, 2} = \frac{- ( - 12 ) \pm 2 17}{2 \cdot 1}

Separate the solutions

r_{1} = \frac{- ( - 12 ) + 2 17}{2 \cdot 1}, r_{2} = \frac{- ( - 12 ) - 2 17}{2 \cdot 1}

r = \frac{- ( - 12 ) + 2 17}{2 \cdot 1} : 6 + 17

r = \frac{- ( - 12 ) - 2 17}{2 \cdot 1} : 6 - 17

The solutions to the quadratic equation are:

r = 6 + 17, r = 6 - 17

0 = 3 x^{2} - 10 x + 6

3 x^{2} - 8 n + 4

x^{2} + 12 x + 23 = 0

x^{2} - 4 x - 5 = 0

x^{2} = 3 x + 7

What are the solutions to the equation r^2-6r+19=6r ?
The solutions to the equation r^2-6r+19=6r are r=6+sqrt(17),r=6-sqrt(17)
Find the zeros of r^2-6r+19=6r
The zeros of r^2-6r+19=6r are r=6+sqrt(17),r=6-sqrt(17)