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Example 7 - Solve 2x2 - 5x + 3 = 0 by completing the square - Solving by completing square

  1. Chapter 4 Class 10 Quadratic Equations
  2. Serial order wise
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Example 7 Solve the equation given in Example 3 (2x2 – 5x + 3 = 0) by the method of completing the square. 2x2 – 5x + 3 = 0 Dividing by 2 (2𝑥2 − 5𝑥 + 3)/2=0/2 2𝑥2/2−5𝑥/2+3/2=0 x2 – 5𝑥/2+3/2=0 We know that (a – b)2 = a2 – 2ab + b2 Here, a = x & – 2ab = (− 5𝑥)/2 – 2xb = (− 5𝑥)/2 – 2b = (− 5)/2 b = (− 5)/(2(−2)) b = 5/4 Now, in our equation x2 – 5𝑥/2+3/2=0 Adding and subtracting (5/4)^2 x2 – 5𝑥/2+3/2+(5/4)^2−(5/4)^2=0 x2 +(5/4)^2– 5𝑥/2+3/2−(5/4)^2=0 (𝑥−5/4)^2 +3/2−(5/4)^2=0 (𝑥−5/4)^2 +3/2−25/16=0 (𝑥−5/4)^2=25/16 − 3/2 (𝑥−5/4)^2=(25 − 3(8))/16 (𝑥−5/4)^2=(25 − 24)/16 (𝑥−5/4)^2=1/16 (𝑥−5/4)^2=(1/4)^2 Cancelling square 𝑥−5/4 = ± 1/4 𝑥−5/4 = ± 1/4 Solving So, the roots of the equation are x = 3/2 & x = 1

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