Mathematics: The equation 2x2 – 5x = –12 is rewritten in the form of 2(x – p)2 + q = 0. what is the value of q?

By lunch you mean launch. 8 hrs = 60 x 8 = 480 minutes 480 + 35 = 515/60 = 103/12 (simplified)...

The equation 2x2 – 5x = –12 is rewritten in the form

almaromeroo13

16.03.2022

$q=\dfrac{71}{8}$

Step-by-step explanation:

The given equation is

2x^2-5x=-12

Rewrite the given equation in the form of

2(x-p)^2+q=0 ... (i)

We need to find the value of q.

The given equation can be rewritten as

$2(x^2-\dfrac{5}{2}x)=-12$

Now, add and subtract square of half of coefficient of x inside the parenthesis.

$2(x^2-\dfrac{5}{2}x+(\dfrac{5}{4})^2-(\dfrac{5}{4})^2)=-12$

$2(x^2-\dfrac{5}{2}x+(\dfrac{5}{4})^2)-2(\dfrac{5}{4})^2)=-12$

$2(x-\dfrac{5}{4})^2-2(\dfrac{25}{16})=-12$

Add 12 on both sides.

$2(x-\dfrac{5}{4})^2-\dfrac{25}{8}+12=0$

$2(x-\dfrac{5}{4})^2+\dfrac{96-25}{8}=0$

$2(x-\dfrac{5}{4})^2+\dfrac{71}{8}=0$ ... (ii)

From (i) and (ii), we get

$q=\dfrac{71}{8}$

Therefore, $q=\dfrac{71}{8}$ .

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