Question

Find the roots of the quadratic equation if they exist by Completely the square 20x² –15x – 10 = 0

Answer 1

Dividing the equation by 20 we get x^2 - 3x/4 - 1/2 = 0 Adding and subtracting (3/8)^2 x^2 - 3x/4 + (3/8)^2 - (3/8)^2 - 1/2 = 0 (x - 3/8)^2 = 9/64 + 1/2                   = 41/64 (8x - 3)/8 = +_√41/√64                 = +_ √41/8 8x - 3 = +_√41 Therefore x = (√41+3)/8   or    (-√41+3)/8

Answer 2

Answer:

Step-by-step explanation:

x = ( 3 ± √41)/8

Given Quadratic equation ,

20x² - 15x - 10 = 0

Divide each term with 20 , we

get

=> x² - (3/4)x - 1/2 = 0

=> x² - 2.x.(3/8) = 1/2

=> x² - 2.x.(3/8) +(3/8)²=1/2+(3/8)²

=> ( x - 3/8 )² = 1/2 + 9/64

=> ( x - 3/8 )² = ( 32 + 9 )/64

=> ( x - 3/8 )² = 41/64

=> x - 3/8 = ± √(41/64)

=> x = 3/8 ± √41/8

=> x = ( 3 ± √41 )/8

x = (3 + √41 )/8

or

x = ( 3 - √41 )/8

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