Completing the square?

x² - 5x = 4

(x - 5/2)² = 41/4

x = (5 ± √41) / 2

Answer: see above

Question Number 1 :

For this equation -x^2 + 5*x + 4 = 0 , answer the following questions :

A. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation -x^2 + 5*x + 4 = 0 is already in a*x^2+b*x+c=0 form.

So we can imply that the value of a = -1, b = 5, c = 4.

1A. Use completing the square to find the root of the equation !

-x^2 + 5*x + 4 = 0 ,divide both side with -1

Which result in x^2 - 5*x - 4 = 0 ,

Which means that the coefficient of x is -5

We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -5/2 = -2.5

Next, we have to separate the constant to form x^2 - 5*x + 6.25 - 10.25 = 0

And it is the same with ( x - 2.5 )^2 - 10.25 = 0

Which can be turned into (( x - 2.5 ) - 3.20156211871642 ) * (( x - 2.5 ) + 3.20156211871642 ) = 0

By opening the brackets we will get ( x - 2.5 - 3.20156211871642 ) * ( x - 2.5 + 3.20156211871642 ) = 0

Just add up the constants in each brackets, and we get ( x - 5.70156211871642 ) * ( x + 0.701562118716424 ) = 0

So we have the answers x1 = 5.70156211871642 and x2 = -0.701562118716424

x^2-5x+4=0

divide -5 by 2, and square it. Then transp0se 4 to the right and add the square of -5/2,

x^2-5x+25/4=-4+25/4

(x-5/2)^2=-16+25/4

(x-5/2)^2=9/4

x-5/2=9/4

x=9/4+5/2

x=19/4

-(xsquared - 5x)+4=0

-x^2+5x+4=0

Equation: -1x^2+5x+4

-(x^2-5/1 x)+4

-(x^2-5/1 x+(5/2)^2)+4+1(5/2)^2

-(x-5/2)^2+4+25/4

-(x-5/2)^2+41/4

-(x-5/2)^2+41/4=0

If you want to solve for x:

-(x-5/2)^2 = -41/4

(x-5/2)^2 = 41/4

(x-5/2)= ± √41/ 2

x= 5/2 ± √41/ 2