How do you solve -2x ^ { 2} = 2x - 4?

2 Answers
Oct 6, 2017

x=1,-2

Explanation:

rearrange to

ax^2+bx+c=0

-2x^2=2x-4

=>2x^2+2x-4=0

divide by 2

x^2+x-2=0

factorise

(x+2)(x-1)=0

giving

x+2=0=>x=-2

x-1=0=>x=1

Oct 6, 2017

x=-2 or x=1

Explanation:

To solve this, you first need to put everything on one side:

-2x^2=2x-4
2x^2+2x-4=0

From here, we can factor 2 out:

2(x^2+x-2)=0

Dividing by two, we get:

x^2+x-2=0

This can then be factorised by finding two numbers that multiply to get -2 and add to get 1. Looking at the factors of 2, you can find these numbers are -1 and 2.

(x-1)(x+2)=0

Now, you have two things multiplied together that equal 0. This means that one of them has to equal 0. To find the values of x for this to happen, we split the two parts:

x-1=0
therefore x=1

OR

x+2=0
therefore x=-2

So, the solution to this equation is x=-2 or x=1