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Solutions of Quadratic Equations by Completing the Square

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• method of completing the square

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In the previous section, you have learnt one method of obtaining the roots of a quadratic equation. In this section, we shall study another method. To implement this method we have certain steps to follow. We will understand the steps with 2x^2+7x-9=0 this example-
1) Make the coefficient of  x^2 as 1. For that we have to divide the whole equation with the coefficient of x^2. In the above example coefficient of x^2 is 2 so will divide the equation with 2, we get, x^2+"7x"/2-9/2=0

2) After that take the constant to RHS. So we get x^2+"7x"/2=9/2.

3) Now take the square of the coefficient of x after multiplying with 1/2, and then add that number to both the sides i.e add: (1/2× "coefficient" "of"   x)^2

Coefficient of x here is 7/2, (1/2×7/2)^2 = (7/4)^2

by adding (7/4)^2 both the sides we get, x^2+"7x"/2+(7/4)^2 = 9/2+(7/4)^2

4) Use (a+b)^2 or (a-b)^2

x^2+"7x"/2+(7/4)^2 = 9/2+(7/4)^2

By obervation we get, c= 9/2 + 49/16

(x+7/4)^2= (72+49)/16

(x+7/4)^2= 121/16

x+7/4 = + or - sqrt 121/16

x+7/4 = + or - 11/4

x+7/4 = 11/4 or -11/4

x=11/4-7/4 or -11/4-7/4

x= 4/4 or -18/4

x= 1 or -9/2

Thus, the roots of 2x^2+7x-9=0  are 1 or -9/2

We can solve more examples using complete square method to understand easily.

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Quadratic Equation part 7 (Solution by Completing Squares) [00:10:10]
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