Question

Using completing the square method, show that the equation x^2-8x+18 =0 has no solution

Answer 1

$\mathfrak{\huge{Answer:}}$

We need to use the completing square method for the equation given as : $\tt{x^{2} - 8x + 18}$

Start applying it.

$\mathfrak{Step\:1}$ Do the half and then the square of the coeffient of x :

Coeffient of x = $\tt{8 = \frac{8}{2} = 4 = 4^{2}}$

$\mathfrak{Step\:2}$ Put them up all in the right sequence :

$\tt{x^{2} - 8x + 4^{2} - 4^{2} + 18 = 0}$

$\mathfrak{Step\:3}$ Make the correct identity :

$\tt{(x - 4)^{2} = 16 - 18}$

$\mathfrak{Step\:4}$ Finally, do the square root on both the sides :

$\tt{x - 4 = \sqrt{(-2)}}$

Now, we know that $\tt{\sqrt{-2}}$ isn't a real number. It's beyond our current knowledge. Thus, the root of this equation, doesn't actually exist !

Hence Proved!

Answer 2

Answer :

Refer the attachment for the answer.

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Let's see how to use completing square method.

For solving such quadratic equations by this method, proceed as follows :

1. Write the given equation in ax^2 + bx + c = 0 form.

2. Considering the first two terms on L.H.S, find the third suitable square term to make the polynomial a perfect sqaure.

3. Add the square term and subtract the same.

4. Write the square of the first three terms and the last two terms.

5. Factorize and equate each factor to zero.

6. Finally, find the value of x.

This are the steps for completing square method.

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