How do you factor and solve -x^2-2x+3 = 0?

3 Answers
Jun 26, 2018

(-x+1)(x+3)=0

-x+1=0 or x+3=0

x=1 or x=-3

Jun 26, 2018

(-x+1)(x+3)=0

Set -x+1=0 => x=1
Set +x+3=0=>x=-3

Taken you through the process step by step

Explanation:

Given: -x^2-2x+3=0

First of all I am going to make a deliberate mistake.

Notice that 1xx3=3 and -3+1=-2

So in error write: (x-3)(x+1) color(red)(larr" Does not give "-x^2)

Lets consider just the x and ignore the potential error about the constant.

(-x-3)(x+1) = -x^2color(red)(-3x-x)-3

Because we have a negative x lets use this to give us
the required -3x+x->-2x

(-x+?)(x+?) rarr" we need "color(magenta)(-3x) so do this:

color(green)((-x+?)(xcolor(magenta)(+3)) = -x^2-3x+?x+(?xx3))

We now need +3 so ?xx3 has to be (color(magenta)(+1))xx(+3)

color(green)((-xcolor(magenta)(+1))(x+3)color(white)("dd") =color(white)("dd") -x^2color(white)("d")ubrace(-3x+x)+3 =0
color(green)(color(white)("dddddddddddddddddddd")-x^2color(white)("dd")-2xcolor(white)("dd")+3=0)

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So the factorisation is (-x+1)(x+3)=0

Set -x+1=0 => x=1
Set +x+3=0=>x=-3

Jun 26, 2018

x = 1, and x = -3

Explanation:

-x^2 - 2x + 3 = 0
Since a + b + c = 0, use shortcut.
The 2 real roots are:
x = 1 , and x = c/a = 3/-1 = -3.

Rule of Shortcut.
If a + b + c = 0, The 2 real roots are: x = 1, and x = c/a
If a - b + c = 0, The 2 real roots are: x = -1, and x = -c/a

Remember this shortcut. It will save you a lot of time and effort.