Question

4x^2+8x+27=88 consider the given equation. in order to solve by completing the square what number should be added to both sides of the equation? how many of the solutions to the equation are positive? what is the approximate value of the greatest solution to the equation rounded to the nearest hundredth?

Answer 1

Answer with explanation:

The given expression is:

 ⇒ 4 x^2+8 x+27=88

Dividing both sides by,4, we get

$\rightarrow x^2 +2 x +\frac{27}{4}=22\\\\\rightarrow (x+1)^2-1 +\frac{27}{4}-22=0\\\\\rightarrow (x+1)^2-\frac{75}{4}=0\\\\\rightarrow (x+1)^2=\frac{75}{4}\\\\x+1=\pm\frac{8.66}{2}\\\\\rightarrow x+1=4.33 \text{or}\rightarrow x+1= -4.33\\\\\rightarrow x=4.33-1\\\\\rightarrow x=3.33\\\\\rightarrow x= -1-4.33\\\\\rightarrow x=-5.33$

→There are two solutions of this equation, one is

 x = 3.33, which is positive

and other, x= -5.33, which is negative.

→As,the expression contains, square of ,(x+1), so, added and subtracted 1 to (x+1)².

→One Solution is Positive.

→Greatest positive Solution , x= 3.33

→Greatest Negative Solution , x=-5.33

Answer 2

the answer will be 0