Answer:
[tex]q=\dfrac{71}{8}[/tex]
Step-by-step explanation:
The given equation is
[tex]2x^2-5x=-12[/tex]
Rewrite the given equation in the form of
[tex]2(x-p)^2+q=0[/tex] ... (i)
We need to find the value of q.
The given equation can be rewritten as
[tex]2(x^2-\dfrac{5}{2}x)=-12[/tex]
Now, add and subtract square of half of coefficient of x inside the parenthesis.
[tex]2(x^2-\dfrac{5}{2}x+(\dfrac{5}{4})^2-(\dfrac{5}{4})^2)=-12[/tex]
[tex]2(x^2-\dfrac{5}{2}x+(\dfrac{5}{4})^2)-2(\dfrac{5}{4})^2)=-12[/tex]
[tex]2(x-\dfrac{5}{4})^2-2(\dfrac{25}{16})=-12[/tex]
Add 12 on both sides.
[tex]2(x-\dfrac{5}{4})^2-\dfrac{25}{8}+12=0[/tex]
[tex]2(x-\dfrac{5}{4})^2+\dfrac{96-25}{8}=0[/tex]
[tex]2(x-\dfrac{5}{4})^2+\dfrac{71}{8}=0[/tex] ... (ii)
From (i) and (ii), we get
[tex]q=\dfrac{71}{8}[/tex]
Therefore, [tex]q=\dfrac{71}{8}[/tex].
