Question

Find the roots of Quadratic equation
5x² - 6x-32 = 0 by the method of " completing the square ".
Please solve it . ​

Answer 1

Answer:

x = (√(809) - 3)/5

Step-by-step explanation:

5x^2 - 6x - 32= 0

divide by 5

x^2 - (6/5)x - 32 = 0

x^2 - 2 × (6/10)x -32 =0

Adding and subtracting (9/25)

x^2 - 2 × (3/5)x + (9/25) -(9/25) -32 = 0

( x + (3/5))^2 -(9/25)-32 =0

(x + (3/5))^2 - (9+25×32)/25 =0

(x +(3/5))^2 -809/25 =0

(x + (3/5))^2 = 809/25

taking square root

x+(3/5) = √(809/25)

x + 3/5 = √809/5

x = √809/5 - 3/5

x = (√809 - 3)/5

Answer 2

Step-by-step explanation:

5x^2-6x-32=0

dividing with 5

x^2-6/5x-32/5=0

sending-32/5 to the right side

x^2-6/5x=32/5

adding (3/5)^2 on both sides

x^2-6/5x+(3/5)^2=32/5+(3/5)^2

expressing it as (x-3/5)^2

(x-3/5)^2=169/25

(x-3/5)=plus or minus√169/5

x=plus or minus√169/5+3/5

x=169+3/5=172/5

or

x=-169+3/5=166/5

here is your answer

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