Solve. 10x 2 + 20 x + 1 = 0?

Question

Solve. 10x 2 + 20 x + 1 = 0

x = (smaller value)

x = (larger value)

Answer 1

10 x ² + 20 x + 1 = 0
x = [ - 20 ± √(400 - 40) ] / 20
x = [ - 20 ± √360 ] / 20
x = [ - 20 ± 6√(10) ] / 20
x = -1 ± (3/10)(√10)

Answer 2

10x 2 + 20 x + 1 = 0
x^2+10x+1/10=0
x^2+10x+25=-1/10 +25
(x+5)^2=249/10
x=+/-sqrt(249/10)-5

Answer 3

10x^2 + 20x + 1 = 0

step 1: (10)(1) = 10
step 2: factors of 10 which add to 20...
{1&10 , 2&5}
does not factor

use the quadratice equation
a = 10 , b = 20 , c = 1

x = [ -b +/- SQRT (b^2 - 4ac) ] / 2a
x = [ -20 +/- SQRT (20^2 - 4(10)(1) ] / 2(10)
x = [ -20 +/- SQRT (360) ] / 20
x = [ -20 +/- 18.97 ] / 20
x = ( -20 + 18.97 ) / 20 or ( -20 - 18.97) / 20
x = -1.03 / 20 or -38.97 / 20
x = -0.0515 or - 1.9485

Answer 4

10x^2 + 20x + 1 =0

x^2 + 2x + 1/10 = 0

x^2 + 2x + (1)^2 = -1/10 + (1)^2

(x +1)^2 = 1/10

(x+1) = square root 1/10

x = 0.3162 - 1 or = -0.31622 -1

= -0.6838 or = -1.3162

Answer 5

use the quadratic formula:
10=a
20=b
1=c

[-b +/- sqrt (b^2 -4ac)] /2a =x

x= [-20 +/- sqrt (400 - (4)(10)(1)) ] /20
x= [-20 +/- sqrt (400 - 40) ] /20
x= [-20 +/- sqrt (360) ] /20
x= [-20 +/- 6sqrt (10) ] /20
x= -1 +/- [6sqrt (10) ] /20
x= -1 +/- 3/10*sqrt (10)

x = -1 + 3/10*sqrt (10)
x = -1 - 3/10*sqrt (10)

These are the two solutions of the equation.