A little confused on this problem.. 4x^2=12x+40
I have to use standard form to solve..
4x^2-12x-40=0
your first dtep is correct :) do you have the standard formula or should i mention it ?
*step
add 40 to the 0 that leaves 4x^2 -12x = 40
4(x^2-3X+10)=0 (x-5)(x+2)=0 x=5 or x=-2
whats actually the confusion about ?
4(x^2-3X+10)=0 (x-5)(x+2)=0 x=5 or x=-2
how did you get the (x-5)(x+2)
@beesknees01 , if you need to use standard formula, then you should not be concerned about how (x-5)(x+2), you'll get the roots directly using the standard formula
@hartnn yea he is right use standard formula
here it goes, Compare your quadratic equation with \(ax^2+bx+c=0\) find \[a=...?\\b=...?\\c=...?\] then the two roots of x are: \(\huge{x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)
It's just in the lesson, the steps are 1. Write in standard 2. Factor quadratic expression 3. set each factor to 0
so, we don't need the standard formula here, we can do it by factorization. for ax^2+bx+c=0, we search for 2 numbers with sum = b and product =ac so, for your question, first factor out 4, 4(x^2-3X+10)=0 (x^2-3X+10)=0 what are 2 numbers with sum =-3 and product =10 ??
i mean product = -10
x=3 and x=10?
oops, nevermind. That was wrong.
can you think of 2 numbers with sum =-3 and product =-10 ??
Im just putting it in there make sure you know the standard formula Ax^2 + Bx + C = 0 so you can apply it to the quadratic formula.
hint : one of the numbers will be negative.
-5 and 2
those are correct! so, we split -3x as -5x+2x we have x^2-5x+2x-10 =0 can you factor out, x from first 2 terms and +2 from other 2 terms ?
x^2-3x-10=0
from this : x^2-3x-10=0 we got this :x^2-5x+2x-10=0 now you can factor out 'x' from x^2-5x, what you get ?
example : if there was a^2+2ab when i factor out 'a' i get a (a+2b)
(x+2)(x-5)=0?
you got how we get (x+2)(x-5)=0 ?? because thats correct...
i found factors that have a sum of -3 and when multiplied equals -10
ok, last step will be to equate them to 0 x+2 =0 , x-5 =0 x = -2, x=5 those are the values of x you require.
any more doubts ?
Nope, thank you very much!!
Join our real-time social learning platform and learn together with your friends!