Question

hey guys.... 10x^2-3x-1=0 solve using completing square method


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Answer 1

Answer:

x = 1/2 and x = -1/5

Please see the attached image

Hope it helps you

Thanks

Answer 2

Hey Miss

Here's the Answer

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Here is a trick to split the terms, suppose we have an equation as ( a x^2 + b x + c )

Lets suppose a = 1

==> x^2 + b x + c

=> x^2 + bx + (b/2)x + c - (b/2)x

=> [ x^2 + bx + (b/2)^2 ] + c - (b/2)^2

We know ( a + b )^2 = a^2 + b^2 + 2ab

=> ( x + b/2 )^2 + c - (b/2)^2

Now similarly

==> 10x^2 - 3x - 1 = 0

Now to change the given equation in standard form we'll divide it by 10

=> x^2 - 0.3x - 0.1 = 0

=> x^2 - 0.3x + (0.3/2)^2 - 0.1 - (0.3/2)^2 = 0

=> ( x - 3/20 )^2 - [ 0.1 + (0.3/2)^2] = 0

=> ( x - 3/20 )^2 = 1/10 + (3/20)^2

=> ( x - 3/20 )^2 = 1/10 + 9/400

=> ( x - 3/20 )^2 = (40 + 9)/400

=> ( x - 3/20 )^2 = 49/400

=> x - 3/20 = ±√(49/400)

=> x - 3/20 = ± (7 / 20)

NOW FROM HERE THERE CAN BE TWO CASES

CASE 1 :

=> x = (7/20 + 3/20)

=> x = (10/20)

=> x = (1/2)

CASE 2 :

=> x = - 7/20 + 3/20

=> x = (3 - 7)/20

=> x = -4/20

=> x = -1/5

So,

x = 1/2 , x = -1/5

HOPE IT HELPS

:)