Question

solve : x²-7√5x-300=0​

Answer 1

Answer:

x_1=15

x_2=-20

Step-by-step explanation:

x^2+5x-300=0

a = 1

b = 5

c = -300

a=1

b=5

c=-300

x=(-b±sqrt(b^2-4ac))/(2a)

x=(-5±sqrt(5^2-4*1*-300))/(2*1)

x=(-5±sqrt(25-4*1*-300))/(2*1)

x=(-5±sqrt(25-4*-300))/(2*1)

x=(-5±sqrt(25--1200))/(2*1)

x=(-5±sqrt(25+1200))/(2*1)

x=(-5±sqrt(1225))/(2*1)

x=(-5±sqrt(1225))/(2)

x=(-5±sqrt(1225))/2

Simplify 1225 by finding its prime factors:

The prime factorization 1225 of is 5^2*7^2

Write the prime factors:

sqrt(1225)=sqrt(5*5*7*7)

Group the prime factors into pairs and rewrite them in exponent form:

sqrt(5*5*7*7)=sqrt(5^2*7^2)

Use the rule sqrt(x^2)=x to simplify further:

sqrt(5^2*7^2)=5*7

5*7=35