Can I get help with these 4 questions please? It is a General Chemistry I review

Question

Can I get help with these 4 questions please? It is a General Chemistry I review?
Thank you! Question 1 26 pts Solve the folowing equaton for x -25 Place the roots for the equaton into the spaces below Root 1 Root 2 Question 2 25 pts Solve the following equation for x x2+3x-4-0 Place the roots for the equation into the spaces below Be sure to place the smaller.cost into the first blank and Root 1 Root 2 Question 3 25 pts Solve the following equation for x 2x2-4x-3- Place the roots for tho equaion into the spaces below Root 1 Root 2

Explanation / Answer

1. x^2/(x+4)^2 = 25

Taking square root of both sides, there are 2 possible equations,

x/x+4 = +5 or x/x+4 = -5

When x/x+4 =5 i.e. x = 5x + 20 i.e. 4x = -20 hence, x = -5

Alternately, x/x+4 = -5 i.e. x = -5x - 20 i.e. 6x = -20 hence, x = -10/3

Hence root1= -5, root 2 = -10/3

2. x^2 + 3x -4= 0

i.e. x^2 + 4x -x -4 = 0

i.e. x(x+4) -1(x+4) = 0

i.e. (x-1)(x+4) = 0

Hence, either x-1 = 0, i.e. x =1

or x+4 = 0, i.e. x=-4

So, root 1 = -4, root 2 =1

3. 2x^2 - 4x -3 = 0

i.e. x^2 - 2x -3/2 = 0

i.e. x^2 - 2x + 1 - 5/2 = 0

i.e. (x-1)^2 = 5/2

i.e. x-1 = +sq rt 5/2 or x-1 = -sq. rt 5/2

Hence, x= 1 + (5/2) or x = 1-(5/2)

So, root 1 = 1-(5/2) and root 2 = 1 + (5/2)

4. x^2/0.25 -x = 1.8 * 10^-5

ie. x^2 = 4.5 * 10^-6 - 1.8 * 10^-5 x

i.e. x^2 + 1.8 * 10^-5 x - 4.5 * 10^-6 = 0

Hence, x = {-(1.8 * 10^-5) + [(1.8 * 10^-5)^2 - 4 * 1 * (- 4.5 * 10^-6)]}/2* 1 = 2.11 * 10^-3

or x = {-(1.8 * 10^-5) - [(1.8 * 10^-5)^2 - 4 * 1 * (- 4.5 * 10^-6)]}/2* 1 = - 4.26 * 10^-3

So, root 1 = - 4.26 * 10^-3 and root 2 = 2.11 * 10^-3

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