Question

How do you solve `-4x^2 + x^2 = -36`?

Answer 1

`x=+-2sqrt(3)`

Explanation:

given:`" "color(green)(-4x^2)color(brown)(+x^2)=-36`

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One way of calculating this

We know that`" "+3 + 1 = +4`

So `" -3-1 = -4`

Write `-4x^2` as `-3x^2-1x^2`

Mathematically should be written as `color(green)(-3x^2-x^2)`
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So we know have:

`color(green)(-3x^2-x^2)color(brown)(+x^2)=-36`

But `-x^2+x^2=0` giving

`-3x^2+0=-36`

`-3x^2=-36`

Divide both sides by `-3`

`(-3)/(-3)x^2=(-36)/(-3)`

Divide one negative number by another negative number and you have a positive answer.

But `(-3)/(-3)=+1" and "(-36)/(-3)= + 12`

`1xx x^2=12`

`x^2=12`

Square root both sides

`sqrt(x^2)=sqrt(3xx2^2)`

`x=+-2sqrt(3)`