solve by completing the square?

Question

1. x^2+x-5=0
2. x^2+16n-7=0

Answer 1

1.. move your 5, to right side of equation by adding 5 to both side..

x^2 +x +1/4 = +5 + 1/4
factoring left side.. into a perfect square. you get

(x+1/2)^2 =21/4

taking sqrt of both sides..

you get x +1/2 =+- (sqrt 21)/2

solve for x.. and obtain
x= - 1/2 +- (sqrt 21)/2

second problem is easier,,use my example to complete the next one... you'll learn more by doing it yourself. try it..

Answer 2

Question 1
(x² + x + 1/4) - 1/4 - 5 = 0
(x + 1/2)² = 21/4
(x + 1/2) = ±√21/2
x = -1/2 ± √21/2
x = -1/2.(1 ± √21)
Question 2
(x² + 16n + 64) - 64 - 7 = 0
(x + 8)² = 71
x + 8 = ±√71
x = - 8 ± √71

Answer 3

x^2+x-5=0
x^2+x=5
x^2+x+1/4=5+1/4
(x+1/2)^2=21/4
x+1/2=sqrt(21)/2
x=1/2-sqrt(21)/2, 1/2+sqrt(21)/2

x^2+16x-7=0
x^2+16x=7
x^2+16x+64=7+64
(x+8)^2=71
x+8=sqrt(71)
x=8-sqrt(71), 8+sqrt(71)

Actually, just realized forgot to rationalize the denominator on the first one. Don't forget to always do that.

Answer 4

x-5=16n-7
x=16n-2
n=1/8+x/16

x^2+x-5=0
x^2+x+.25-5.25=0
(x+0.5)^2-5.25=0
x=SQRT(5.25)-.5
x~= 1.79 or 2.79

can solve n from above