Question
Solve the quadratic equation
Solve using the quadratic formula
Solve by completing the square
Solve using the PQ formula
p1=−21+7165,p2=2−1+7165
Alternative Form
p1≈−45.458314,p2≈44.458314
Evaluate
p2+p+1=2022
Move the expression to the left side
p2+p−2021=0
Substitute a=1,b=1 and c=−2021 into the quadratic formula p=2a−b±b2−4ac
p=2−1±12−4(−2021)
Simplify the expression
More Steps

Evaluate
12−4(−2021)
1 raised to any power equals to 1
1−4(−2021)
Multiply the numbers
More Steps

Evaluate
4(−2021)
Multiplying or dividing an odd number of negative terms equals a negative
−4×2021
Multiply the numbers
−8084
1−(−8084)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+8084
Add the numbers
8085
p=2−1±8085
Simplify the radical expression
More Steps

Evaluate
8085
Write the expression as a product where the root of one of the factors can be evaluated
49×165
Write the number in exponential form with the base of 7
72×165
The root of a product is equal to the product of the roots of each factor
72×165
Reduce the index of the radical and exponent with 2
7165
p=2−1±7165
Separate the equation into 2 possible cases
p=2−1+7165p=2−1−7165
Use b−a=−ba=−ba to rewrite the fraction
p=2−1+7165p=−21+7165
Solution
p1=−21+7165,p2=2−1+7165
Alternative Form
p1≈−45.458314,p2≈44.458314
Show Solution
