Question

$\pink{\sf 2x^{2} -7x + 3 = 0}$(solve by complete squaring method)​

Answer 1

SOLUTION :-

=>Given that, 2x² - 7x + 3 = 0 .

=>2x²/2 - 7x/2 + 3/2 = 0/2 ------(Divide by 2 on each sides).

=>.°. x² - 7x/2 + 3/2 = 0

=>.°. x² - 7x/2 = -3/2

=>Add 9/4 on each sides,

=>x² - 7x/2 + 9/4 = -3/2 + 9/4

=>x² - 7x/2 + 3/2 = -3/2 + 9/4

=>(x - 3/2)² = -6 + 9/4

=>(x -3/2)² = 3/4

=>x - 3/2 = √3/4

=>x - 3/2 = ± √3/2

=> x - 3/2 = √3/2 or x - 3/2 = - √3/2

=> x = 3+√3 / 2 or x = -3+√3 / 2

Answer 2

$hello$

Given : 2x² –7x + 3 = 0

On dividing the whole equation by 2,

(x² - 7x/2 + 3/2) = 0

Shift the constant term on RHS

x² - 7x/2 = - 3/2

Add square of the ½ of the coefficient of x on both sides

On adding (½ of 7/2)² = (7/4)² both sides

x² - 7x/2 + (7/4)²= - 3/2 + (7/4)²

Write the LHS in the form of perfect square

(x - 7/4)² = - 3/2 + 49/16

[a² - 2ab + b² = (a - b)²]

(x - 7/4)² = (-3 × 8 + 49)/16

(x - 7/4)² = (-24 + 49)/16

(x - 7/4)² = 25/16

On taking square root on both sides

(x - 7/4) = √(25/16)

(x - 7/4) = ± 5/4

On shifting constant term (-7/4) to RHS

x = ± 5/4 + 7/4

x = 5/4 + 7/4

[Taking +ve sign]

x = (5 +7)/4

x = 12/4

x = 3

x = - 5/4 + 7/4

[Taking -ve sign]

x = (- 5 + 7)/4

x = 2/4

x = 1/2

Hence, the roots of the given equation are 3 & ½.