What are the solutions to the equation 2r=5-r^2 ?

The solutions to the equation 2r=5-r^2 are r=-1-sqrt(6),r=sqrt(6)-1

Find the zeros of 2r=5-r^2

The zeros of 2r=5-r^2 are r=-1-sqrt(6),r=sqrt(6)-1

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2 r = 5 - r^{2}

r = - 1 - 6, r = 6 - 1

Decimal Notation

r = - 3.44948 \dots, r = 1.44948 \dots

Solution steps

2 r = 5 - r^{2}

Switch sides

5 - r^{2} = 2 r

Move

2 r

to the left side

5 - r^{2} - 2 r = 0

Write in the standard form

a x^{2} + b x + c = 0

- r^{2} - 2 r + 5 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 ( - 1 ) \cdot 5}{2 ( - 1 )}

(- 2)^{2} - 4 (- 1) \cdot 5 = 26

r_{1, 2} = \frac{- ( - 2 ) \pm 2 6}{2 ( - 1 )}

Separate the solutions

r_{1} = \frac{- ( - 2 ) + 2 6}{2 ( - 1 )}, r_{2} = \frac{- ( - 2 ) - 2 6}{2 ( - 1 )}

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

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

The solutions to the quadratic equation are:

r = - 1 - 6, r = 6 - 1

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

r^{2} + 4 r + 3

3 x^{2} + 2 = 8 x

0 = 12 x^{2} - 160 x + 400

- x^{2} + 49 = - 15

What are the solutions to the equation 2r=5-r^2 ?
The solutions to the equation 2r=5-r^2 are r=-1-sqrt(6),r=sqrt(6)-1
Find the zeros of 2r=5-r^2
The zeros of 2r=5-r^2 are r=-1-sqrt(6),r=sqrt(6)-1