find the roots of the following quadratic equations if they exist. X square + 5 is equals to minus 6
Answers
Step-by-step explanation:
Roots of given equationx^2+5=-6xx
2
+5=−6x are -1 and -5.
Step-by-step explanation:
Given:
x^2+5=-6xx
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=-5x
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(a+b)
2
=a
2
+2ab+b
3
In our equation a = xa=x
2ab = 6x2ab=6x
but 6x6x can be written as 2\times 3x2×3x
So we can say that third term c=3c=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;
\begin{gathered}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\end{gathered}
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;
\begin{gathered}\sqrt{(x+3)^2} = \sqrt{4} \\\\x+3= \sqrt{4}\end{gathered}
(x+3)
2
=
4
x+3=
4
Now root have 2 values 1 positive and 1 negative.