1+7/11 = 11/11+7/11 = 18/11
2+1/2 = 4/2+1/2 = 5/2
(18/11)/(5/2) = (18/11)*(2/5) = 36/55
1) given x^4 + 95x^2 - 500
2) split in two factors with common factor term x^2: (x^2 + )(x^2 - )
3) find two numbers that add up 95 and their product is - 500:
=> 100*(-5) = - 500 and 100 - 5 = 95
=> (x^2 + 100)(x^2 - 5)
4) factor x^2 - 5 = (x + √5) (x - √5)
5) write the prime factors: (x^2 + 100) (x + √5) (x -√5)
6) find the solutions:
x^2 + 100 = 0 => not possible
x + √5 = 0 => x = - √5
x - √5 = 0 => x = √5
Answer: x = √5 and x = - √5
16 it is as easy as multiplying
Remark
Multiply both sides of the equation by 25. Then you have an equation that you have already done probably.
Step One
Multiply both sides of the equation by 25
1 * (20 - t) = 4t - (3/5) * 25 Every part of the equation must be multiplied by 25
(20 - t) = 4t - 75/5 3*25/5 = 75/5
20 - t = 4t - 15 Add t to both sides
20 - t + t =4t + t - 15 Combine like terms
20 = 5t - 15 Add 15 to both sides
20 + 15 = 5t - 15 + 15 Combine like terms
35 = 5t Divide by 5
35/5 = 5t/5 Switch sides
t = 7 Answer
