What are the solutions to the equation p^2+p/3 = 1/6 ?

The solutions to the equation p^2+p/3 = 1/6 are p=(-1+sqrt(7))/6 ,p=-(1+sqrt(7))/6

Find the zeros of p^2+p/3 = 1/6

The zeros of p^2+p/3 = 1/6 are p=(-1+sqrt(7))/6 ,p=-(1+sqrt(7))/6

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p^{2} + \frac{p}{3} = \frac{1}{6}

p = \frac{- 1 + 7}{6}, p = - \frac{1 + 7}{6}

Decimal Notation

p = 0.27429 \dots, p = - 0.60762 \dots

Solution steps

p^{2} + \frac{p}{3} = \frac{1}{6}

Find Least Common Multiplier of

3, 6 : 6

Multiply by LCM=

6

p^{2} \cdot 6 + \frac{p}{3} \cdot 6 = \frac{1}{6} \cdot 6

Simplify

6 p^{2} + 2 p = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

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

p_{1, 2} = \frac{- 2 \pm 2 7}{2 \cdot 6}

Separate the solutions

p_{1} = \frac{- 2 + 2 7}{2 \cdot 6}, p_{2} = \frac{- 2 - 2 7}{2 \cdot 6}

p = \frac{- 2 + 2 7}{2 \cdot 6} : \frac{- 1 + 7}{6}

p = \frac{- 2 - 2 7}{2 \cdot 6} : - \frac{1 + 7}{6}

The solutions to the quadratic equation are:

p = \frac{- 1 + 7}{6}, p = - \frac{1 + 7}{6}

x^{2} = 1600

(2 x + 1)^{2} = 64

(2 x + 1)^{2} = 48

(x + 3)^{2} = 17

(x + 3)^{2} = 24

What are the solutions to the equation p^2+p/3 = 1/6 ?
The solutions to the equation p^2+p/3 = 1/6 are p=(-1+sqrt(7))/6 ,p=-(1+sqrt(7))/6
Find the zeros of p^2+p/3 = 1/6
The zeros of p^2+p/3 = 1/6 are p=(-1+sqrt(7))/6 ,p=-(1+sqrt(7))/6