SOLUTION: To Whom It May Concern: Your assistance is greatly appreciated. Didn't have the textbook info yesterday when I submitted these questions. The questions are from a quiz th

Algebra ->  Equations -> SOLUTION: To Whom It May Concern: Your assistance is greatly appreciated. Didn't have the textbook info yesterday when I submitted these questions. The questions are from a quiz th      Log On


   

Question 67703This question is from textbook Algebra and Trigonometry with Analytic Geometry
: To Whom It May Concern:
Your assistance is greatly appreciated.
Didn't have the textbook info yesterday when I submitted these questions.
The questions are from a quiz that I took for my online course.

Find the value of k that completes the square for x2 + 10x + k?

Use completing the square or the quadratic formula to find the solutions to the equation x2 – 4x + 2 = 0

Find the solutions to the equation: x2 + 2x + 5 = 0?

Find the solutions to the equation: x + 7/x = 8?

Solve the equation: x – 3 – sqrt x – 1 = 0?

Solve the equation: x + 2 – 2 sqrt x + 2 = 0?

Solve the inequality 2 | x – 10 | < 3 and express the solution as an interval?
Please get back to me ASAP since I'm studying for my final exam.

 This question is from textbook Algebra and Trigonometry with Analytic Geometry

Answer by ybalkas(3) About Me  (Show Source):
You can put this solution on YOUR website!
1) x^2 + 10x +25 , let k=25 then (x+5)^2
2) x^2 – 4x + 4-4+2 = 0 (add and subtract 4)then (x-2)^2-2=0 then (x-2)^2=2
(x-2)=+sqrt(2) or (x-2)=-sqrt(2)
x1=2+sqrt(2) or x2=2-sqrt(2)
3)x2 + 2x + 5 = 0? then x^2+2x+1+4= then (x+1)^2=-4 so no solutuin.
or check discriminant D= 2^2-4.5.1=-16
4)x+7/x=8 then x^2-8x+7=0 then (x-7)(x-1)=0 then x1=7 or x2=1
5)Solve the equation: x – 3 – sqrt x – 1 = 0?
x-3=sqrt(x-1) take square of both sides then x^2-6x+9=x-1 then x^2-7x+10=0 then factorize (x-2)(x-5)=0 x1=5 or x2=2 check both solutions then only 5 satisfies the original equation.
6)x + 2 – 2 sqrt x + 2 = 0? x+2=2 sqrt x + 2 then take square of both sides, x^2+4x+4=4(x+2) then x^2+4x+4=4x+8 then x^2=4 the x1=2 or x2=-2 check both solutions. If x1=2 then 4-2.2=0 satisfies x2=-2 also satisfies so solutions {2 ,-2}
7)2 <| x – 10 | < 3
then there are two conditions I) -3 the second condition 2< x-10 then x> 12 or 2 <-x+10 then
7