Discover new information and get your questions answered with IDNLearn.com. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

Complete the square x^2+4x+8

Sagot :

[tex]x^2 +4x +8\\\\= x^2 + 2 \cdot 2 \cdot x + 2^2 - 2^2 +8\\\\=(x+2)^2 - 4 +8 \\\\= (x+2)^2 +4[/tex]

Answer:

2(x+2)

Step-by-step explanation:

STEPS USING DIRECT FACTORING METHOD

x  

2

+4x+8

Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x  

2

+Bx+C=0.

x  

2

+4x+8=0

Let r and s be the factors for the quadratic equation such that x  

2

+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the product of factors rs=C

r+s=−4

rs=8

Two numbers r and s sum up to −4 exactly when the average of the two numbers is  

2

1

∗−4=−2. You can also see that the midpoint of r and s corresponds to the axis of symmetry of the parabola represented by the quadratic equation y=x  

2

+Bx+C. The values of r and s are equidistant from the center by an unknown quantity u. Express r and s with respect to variable u.

r=−2−u

s=−2+u

To solve for unknown quantity u, substitute these in the product equation rs=8

(−2−u)(−2+u)=8

Simplify by expanding (a−b)(a+b)=a  

2

–b  

2

 

4−u  

2

=8

Simplify the expression by subtracting 4 on both sides

−u  

2

=8−4=4

Simplify the expression by multiplying −1 on both sides and take the square root to obtain the value of unknown variable u

u  

2

=−4

u=±  

−4

=±2i

The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.

r=−2−2i

s=−2+2i