Intermediate Algebra

25(5m+2/m)^2 -20(5m+2/m) +4

2x^-2 -3x^-1 -2 = 0

Each equation has 2 answers

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1.
25(5m+2/m)² -20(5m+2/m) +4       ← This is a quadratic expression in (5m+2/m).
                                                      You can see this if you let u=5m+2/m.
                                                      Then the expression becomes:
                                                      25u² - 20u + 4 which factors to (5u - 2)².
                                                      You don't identify what the instructions are.
                                                      So, you'll have to take it from here.


2.
     2x⁻² - 3x⁻¹ - 2 = 0                       ← You can get rid of the negative exponents
                                                         by multiplying both sides by x².
x²(2x⁻² - 3x⁻¹ - 2) = 0·x²
     2x⁰ - 3x¹ - 2x² = 0                       ← by the laws of exponents
  -2x⁰ + 3x¹ + 2x² = 0                       ← multiplied both sides by -1
        2x² + 3x - 2 = 0
        (2x-1)(x+2) = 0
   I'm sure you can take this
       the rest of the way.


Have a good one!!!
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25(5m+2/m)^2 -20(5m+2/m) +4
[5*(5m+2/m)]^2 - 2*5(5m+2/m) +2^
[5(5m+2/2)-2]^2

If this one is equal to 0, it has only one answer, if it is greater than 0 it has 2 answers and if it is lower than 0, it has only one irreal answer ( of the x + yi form, where i=sqrt(-2) )

use the following formula: a^2 - 2ab + b^2 = (a-b)^2.
also, this one helps: a^2 + 2ab + b^2 = (a+b)^2