#### Question

Find the roots of the following quadratic equations (if they exist) by the method of completing the square.

x^{2} - 4ax + 4a^{2} - b^{2} = 0

#### Solution

We have to find the roots of given quadratic equation by the method of completing the square. We have,

x^{2} - 4ax + 4a^{2} - b^{2} = 0

Now shift the constant to the right hand side,

x^{2} - 4ax = b^{2} - 4a^{2}

Now add square of half of coefficient of x on both the sides,

x^{2} - 2(2a)x + (2a)^{2} = b^{2} - 4a^{2} + (2a)^{2}

We can now write it in the form of perfect square as,

(x - 2a)^{2} = b^{2}

Taking square root on both sides,

`(x-2a)=sqrt(b^2)`

So the required solution of x,

x = 2a ± b

x = 2a + b, 2a - b

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Roots of the Following Quadratic Equations (If They Exist) by the Method of Completing the Square. X2 - 4ax + 4a2 - B2 = 0 Concept: Solutions of Quadratic Equations by Completing the Square.