What are the solutions to the equation 6r+r^2=27 ?

The solutions to the equation 6r+r^2=27 are r=3,r=-9

Find the zeros of 6r+r^2=27

The zeros of 6r+r^2=27 are r=3,r=-9

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6 r + r^{2} = 27

r = 3, r = - 9

Solution steps

6 r + r^{2} = 27

Move

27

to the left side

6 r + r^{2} - 27 = 0

Write in the standard form

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

r^{2} + 6 r - 27 = 0

Solve with the quadratic formula

r_{1, 2} = \frac{- 6 \pm 6 ^{2} - 4 \cdot 1 \cdot ( - 27 )}{2 \cdot 1}

6^{2} - 4 \cdot 1 \cdot (- 27) = 12

r_{1, 2} = \frac{- 6 \pm 12}{2 \cdot 1}

Separate the solutions

r_{1} = \frac{- 6 + 12}{2 \cdot 1}, r_{2} = \frac{- 6 - 12}{2 \cdot 1}

r = \frac{- 6 + 12}{2 \cdot 1} : 3

r = \frac{- 6 - 12}{2 \cdot 1} : - 9

The solutions to the quadratic equation are:

r = 3, r = - 9

4 x^{2} - 16 x - 20 = 0

3 q^{2} - 110 q + 900 = 0

(x - 2) (x + 3) = 2 x^{2} - 4 x

9 x^{2} - 9 x + 19 = 0

x^{2} + 2 x - 12 = - 12

What are the solutions to the equation 6r+r^2=27 ?
The solutions to the equation 6r+r^2=27 are r=3,r=-9
Find the zeros of 6r+r^2=27
The zeros of 6r+r^2=27 are r=3,r=-9