What are the roots for the function x^2+4x-3=0

Question

campbell_st · Answer

well you need the general quadratic formula of you can complete the square... which do you find easier...?

anonymous · Answer

the answers given was
a. x= -2,6 
b. x= -4, 12
c. x= -2+-sqrt(7)
d. x=2+-21sqrt(2)

I'm sure a and b is out. How about c and d? how do i do this when there is sqrt?

campbell_st · Answer

well its quite simple... and no need to guess... 


you can solve by 

1. completing the square

2. using the general quadratic formula

it depends on which you are more comfortable with ..

anonymous · Answer

note, please don't get confused, +- means the plus is on top and the minus is below the + sign

anonymous · Answer

i prefer the completing the square method

campbell_st · Answer

ok... so rewrite the quadratic as

$$x^2 + 4x = 3$$

what do you need to add to the left hand side to get a perfect square..?

anonymous · Answer

im not sure... A bit confusing

campbell_st · Answer

ok... so a perfect square is 

$$(x +b)^2 = x^2 + 2bx + b^2$$

so what you need to do is halve the coefficient of the middle term then square it.. 

so in you question what is half of 4 squared...?

anonymous · Answer

2

campbell_st · Answer

well have of the coefficient is 2

then squared is 4

so you need to add 4 to both sides of the equation 

$$x^2 + 4x + 4 = 3 + 4$$

this can be simplified to 

$$(x + 2)^2 = 7$$


so now all you need to do is solve for x. 

hope this helps.

anonymous · Answer

what if i want to use the  the general quadratic formula?

campbell_st · Answer

you'll get the same result

you can also get a clue using the discriminant... if you know what it is

campbell_st · Answer

so do you know how to solve it from here...?

anonymous · Answer

yes i just solved it using the  completing the square which is the answer is c

anonymous · Answer

i tried using the general quadratic formula but i didt get the answer

campbell_st · Answer

ok... so lets get back to completing the square

$$(x + 2)^2 = 7$$

whats the 1st step

campbell_st · Answer

and your solution using the GQF maybe caused by not knowing how to simplify a radical

anonymous · Answer

i would like to know when do u use this formula $$(x+b)^{2}=x ^{2}+2bx+b ^{2}$$? because i only recall how to do (x+_) (x-_). When must this be used and when must that formula u given me be used?

campbell_st · Answer

the left hand side is a perfect square, the right hand side is the expansion.

the left hand side is 

(x + b)(x + b)

campbell_st · Answer

what you recall is the difference of 2 squares

$$(x -a)(x + a) = x^2 - a^2$$

campbell_st · Answer

ok, so lefts solve the equation above... whats the 1st step

campbell_st · Answer

its 

$$(x + 2)^2 = 7$$

campbell_st · Answer

any idea on how to start solving the equation...?

anonymous · Answer

yes i solved it. again the  general quadratic formula i didt get it. the answer is not the same

campbell_st · Answer

all you need to do with the complete the square method is 

$$(x +2)^2 = 7$$

take the square root of both sides

$$x + 2 = \pm \sqrt{7}$$

subtract 2 from both sides

$$x = -2 \pm \sqrt{7}$$

anonymous · Answer

i got it... thank u campbell... you were so helpful