Question

Solve for x by the method of completing the square
2x²- 5x-3=0​

Answer 1

Given :-

• Quadratic equation : 2x² - 5x - 3 = 0.

To Find :-

• What is value of x.

Solution :-

Given that, 2x² - 5x - 3 = 0

➡ 2x² - 5x = 3

[ Divide by 2 on each sides. ]

➡ 2x²/2 - 5x/2 = 3/2

➡ x² - 5x/2 = 3/2

[ Adding (5/4)² on each sides, We get : ]

➡ x² - 5x/2 + (5/4)² = 3/2 + (5/4)²

[ ( a² - ab + b² ) = (a - b)² ]

➡ (x - 5/4)² = 3/2 + 25/16

➡ (x - 5/4)² = 49/16

➡ x - 5/4 = ±√49/16

➡ x - 5/4 = ± 7/4

➡ x + 5/4 = 7/4 Or x - 5/4 = 7/4

➡ x = -1/2 , 3.

Hence,

• The value of x is (-1/2 , 3).