I know this is a simple question but for some reason im getting stumped:

Question: x-3=-x^2
atempt: (x^2)+x = 3

x^2 + x + 1/4= 3(4) + 1/4

(x+1/2)^2= 3

root everthing

x+1/2= root 3
x=+,- root 3 -1/2

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symbolipoint
Homework Helper
Gold Member
Your initial algebraic steps were wrong. From the start, you should obtain:

from which the solutions are very plain (what?).

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-1x2 = 3???

symbolipoint
Homework Helper
Gold Member
Trying again: Your first steps were wrong. You should first obtain

$$$x^2 + x - 3 = 0$$$

and then you can use general solution to quadratic equation OR complete square.

Well, i don't really understand what u tried to do.

$$x-3=-x^{2}=> x^{2}+x-3=0$$ Now do you could either try to factor this out, or apply directly the quadratic formula, do you know it?

$$x_1_,_2=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$$

In this particular case, i don't think it will factor nicely, so it is better to use the quadratic formula i provided u with.
Can u go from here?

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sry im only in gr 11 and this was how i was taught... and that formula was never taught to me

sry im only in gr 11 and this was how i was taught... and that formula was never taught to me
Well, you better learn it then, because not always will you be able to factor a quadratic eq. nicely.

The general form of a quadratic equation is

$$ax^{2}+bx+c=0$$ so now can you figure out what a,b and c are in your problem?

oo i do know that thats the form i write my solution as, but for my question i stated above i dont know what im doing wrong to keep me from reaching that formula

oo i do know that thats the form i write my solution as, but for my question i stated above i dont know what im doing wrong to keep me from reaching that formula
Aha i gotch ya!

$$x^2 + x = 3=>x^{2}+2x\frac{1}{2}+\frac{1}{4}-\frac{1}{4}=3=>(x+\frac{1}{2})^{2}=3+\frac{1}{4}=>(x+\frac{1}{2})^{2}=\frac{13}{4}$$

You forgot to add that 1/4 to the 3 on your right hand side.
Well, now you know what to do right?

Integral
Staff Emeritus
Gold Member
I know this is a simple question but for some reason im getting stumped:

Question: x-3=-x^2
atempt: (x^2)+x = 3

x^2 + x + 1/4= 3(4) + 1/4

(x+1/2)^2= 3

root everthing

x+1/2= root 3
x=+,- root 3 -1/2
Where did the bolded factor of 4 come from?

You should have.

$$(x+ \frac 1 2)^2 = 3 \frac 1 4$$

that was just multiplying the denominator by 4 so i could add fractions

that was just multiplying the denominator by 4 so i could add fractions
Well you should have multiplied then both the denominator and the numerator by 4.

yea i know i just was too lazy to type it out >.<

yea i know i just was too lazy to type it out >.<
Well, that's why you got the wrong result then. Better not be lazy!