Question

find the roots of quadratic equation X square + 5 is equals to minus 6 x by the method of completing square​

Answer 1

Answer:

x2 +5=-6x

x2+6x+5=0

by completing square

coefficient of x=6

it's half=6/2=3

it's square=(3)2

add-on both side

x2+6x+5+(3)2=(3) 2

Answer 2

Roots of given equation$x^2+5=-6x$ are -1 and -5.

Step-by-step explanation:

Given:

$x^2+5=-6x$

We need to find the roots of the quadratic equation by the method of completing square​.

Solution:

On Solving the equation we get;

$x^2+6x=-5$

Now we can see the co efficient of 'x' is 6.

Now Complete square formula is;

$(a+b)^2= a^2+2ab+b^3$

In our equation $a = x$

$2ab = 6x$

but $6x$ can be written as $2\times 3x$

So we can say that third term $c=3$

Hence From above we can say that to make complete square we need to add both side by 9.

Adding both side by nine we get;

$x^2+6x+9=-5+9\\\\x^2+3x+3x+9=4\\\\x(x+3)+3(x+3)=4\\\\(x+3)(x+3)=4\\\\(x+3)^2=4$

Taking square root on both side we get;

$\sqrt{(x+3)^2} = \sqrt{4} \\\\x+3= \sqrt{4}$

Now root have 2 values 1 positive and 1 negative.

Hence we can say

$x=-3+\sqrt4}= -3+2=-1\\ \\OR\\\\x=-3-\sqrt4}= -3-2=-5$

Hence Roots of given equation are -1 and -5.