Is this right?

Question

Solve by completing the square:

x^2 = 5x + 2

I think the answer is:

5+- sqrt33/4 ?????? is that correct?

Answer 1

x^2=5x+2
=>x^2-5x-2=0
=>x^2-2.x,5/2+(5/2)^2-(5/2)^2-2=0
=>(x-5/2)^2-33/4=0
=>(x-5/2)^2-(sqrt33)/2]^2=0
=>(x-5/2+(sqrt33)/2)(x-5/2-(sqrt33)/2]=0
therefore,x=5+-(sqrt33)/2
So your answer is correct.(sqrt)33/4 and (sqrt33)/2 is same

Answer 2

Move the 5x to the left side:

x^2 - 5x = 2

Now you need to figure out a number to add to both sides so that the left will be a perfect square. In other words, you want the left to be in the form (x - A)^2. You need to think about everything you know from factoring and doing FOIL.... what can you add to x^2 - 5x so that you can factor it into (x - A)(x - A). Hint: divide 5 by 2 and square the result.

x^2 - 5x + (5/2)^2 = 2 + (5/2)^2

Simplfy:

(x - 5/2)^2 = 8/4 + 25/4
(x - 5/2)^2 = 33/4

Take square root of both sides:

x - 5/2 = (sq rt 33)/2

Isolate x:
x = 5/2 + (sq rt 33)/2
x = [5 + (sq rt 33)]/2

It looks like you forgot to take the square root of the denominator... and both the 5 and the sq rt 33 are in the numerator (can't tell if that's what you meant but the way you have typed it, the 5 is not beind divided by 2). It does look like you know how to complete the square and just need to be careful when combining like terms & simplifying. Thumbs up! ;-)

Answer 3

I haven't done this in a long time, see if what I'm doing makes sense:

x^2 - 5x= 2

x^2 - 5x + 25/4 = 8/4 + 25/4

(x- 5/2)^2 = 33/4

x- 5/2 = +-sqrt 33/4
x= 5/2 +-sqrt 33/4

Answer 4

Take the qn. as x^2=5x+2
x^2-5x-2=0

Formula: x= (-b+-(b^2-4ac)^1/2)/2a

where a=1;b= -5;c= -2

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

= (5+-(25+8)^1/2)/2

= (5+-(33^1/2))/2

= (5+-5.74)/2

= (5+5.74)/2 0r (5-5.74)/2

= 5.37 or -0.37