# Solve the equation given in Example 3 by the method of completing the square

**Solution:**

Let us solve the equation using the method of completing the square.

Given, 2x^{2} - 5x + 3 = 0

Step1: Rewrite the equation in the form of ax^{2} + bx = c

⇒ 2x^{2} - 5x = - 3

Step 2: Divide the coefficient of x2 by the equation.

⇒ x^{2} - 5/2x = - 3/2

Step 3: Divide the coefficient of x by 2 and then add the square of x/ 2 to both the sides of the equation.

⇒ x^{2} - 5/2x + (5/ 4)2 = - 3/2 + (5/ 4)2

Step 4: Solve the equation using the algebraic identity (a - b)^{2} = a^{2} - 2ab + b^{2}

⇒ (x - 5/4)^{2} = 1/16

Step 5: Taking square root on both the sides.

⇒ x - 5/4 = ± ¼

Step 6: Add 5/4 to both the sides.

⇒ x - 5/4 + 5/4 = 5/ 4 ± ¼

⇒ x = 5/ 4 - ¼ or 5/ 4 + ¼

⇒ x = 4/4 or 6/4

⇒ x = 1 or 3/2

The solution of the equation 2x^{2} - 5x + 3 = 0 is 1, 3/2 using the method of completing the square

ā Check: NCERT Solutions for Class 10 Maths Chapter 4

## Solve the equation given in Example 3 by the method of completing the square

**Summary: **

The solution for the equation 2x^{2} - 5x + 3 = 0, given in Example 3 by the method of completing the square is 1 or 3/2

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