Rewrite the equation by completing the square X^2+6x+9=0 (X+?)^2=?
Mathematics · High School · Thu Feb 04 2021
Answered on
Given the quadratic equation:
x^2 + 6x + 9 = 0
Rewrite the equation by completing the square.
Solution:
The given equation is a perfect square quadratic equation, whereas it can easily be determined due to the fact that the first term and the last term is a perfect square. Hence, we can write the factor as,
( x + 3 )^2 or ( x + 3 ) ( x + 3 )
In order to check if the factor is true, we simply need to apply the FOIL Method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (x)(x)
=x^2
First term of the first equation multiplied to the first term of the second equation.
=(x)(3)
= 3x
First term of the first equation multiplied to the last term of the second equation.
=(3)(x)
=3x
Last term of the first equation multiplied to the first term of the second equation.
=(3)(3)
= 9
Last term of the first equation multiplied to the fast term of the second equation.
= x^2 + 3x + 3x + 9
= x^2 + 6x + 9
Final answer:
= (x + 3)^2