Respuesta :
Given:
The equation is:
[tex]x^2+5x=2[/tex]
To find:
The solution of the given equation by completing the square.
Solution:
We have,
[tex]x^2+5x=2[/tex]
We need to add the square of half of the coefficient of x on both sides.
Adding [tex]\left(\dfrac{5}{2}\right)^2[/tex] on both sides, we get
[tex]x^2+5x+\left(\dfrac{5}{2}\right)^2=2+\left(\dfrac{5}{2}\right)^2[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=2+\dfrac{25}{4}[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{8+25}{4}[/tex]
[tex]\left(x+\dfrac{5}{2}\right)^2=\dfrac{33}{4}[/tex]
Taking square root on both sides, we get
[tex]x+\dfrac{5}{2}=\pm \sqrt{\dfrac{33}{4}}[/tex]
[tex]x=\pm \dfrac{\sqrt{33}}{2}-\dfrac{5}{2}[/tex]
[tex]x=\dfrac{\pm \sqrt{33}-5}{2}[/tex]
[tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex]
Therefore, the solutions of the given equation are [tex]x=\dfrac{\sqrt{33}-5}{2}[/tex] and [tex]x=\dfrac{-\sqrt{33}-5}{2}[/tex].
