Question

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

2x² – 10x + 5 = 0

Answer 1

Compare it with equation

ax2 + bx + c = 0

a = 2, b = -10, c = 5

D = b2 - 4ac

= (-10)2 - 4(2) (5)

= 100 - 40

= 60

`x = (-b+-sqrtD)/(2a)`

`=> (-(-10)+-sqrt60)/(2xx2)`

`=> (10 +- sqrt15xx4)/4`

`=> (10 +- 2sqrt15)/4`

`= (10 +- 2xx3.875)/4`

`=\cancel2(5+-3.875)/\cancel4`

`x = (5+3.875)/2`

`8.875/2 = 4.4375 = 4.44`

or

x = `5 - 3.875/2 = 1.125/2 = 0.5625`

x = 4.44 or 0.56

Working note:

`sqrt15`

`sqrt16-1`

`4-1/(2xx4)`

`4-(1xx125)/(8xx125)`

`4-125/1000`

4 - 0.125

= 3.875