Solve p^2 + p +1=2022

Evaluate

p^{2} + p + 1 = 2022

Move the expression to the left side

p^{2} + p - 2021 = 0

Substitute a= 1,b= 1 and c= - 2021 into the quadratic formula p = \frac{- b \pm b ^{2} - 4 a c}{2 a}

p = \frac{- 1 \pm 1 ^{2} - 4 ( - 2021 )}{2}

Simplify the expression

More Steps

p = \frac{- 1 \pm 8085}{2}

Simplify the radical expression

More Steps

p = \frac{- 1 \pm 7 165}{2}

Separate the equation into 2 possible cases

p = \frac{- 1 + 7 165}{2} p = \frac{- 1 - 7 165}{2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

p = \frac{- 1 + 7 165}{2} p = - \frac{1 + 7 165}{2}

Solution

p_{1} = - \frac{1 + 7 165}{2}, p_{2} = \frac{- 1 + 7 165}{2}

Alternative Form

p_{1} \approx - 45.458314, p_{2} \approx 44.458314

Solve the quadratic equation