Question

How do you solve `4x^2=25`?

Answer 1

`x=+-5/2`

Explanation:

Use the `color(gold)("golden rule"` of Algebra

`"What we do on one side,must be done on the other side also"`

Our aim is to isolate `x` to find its value

`color(blue)(4x^2=25`

Divide both sides by `4`

`rarr(cancel4x^2)/cancel4=25/4`

`rarrx^2=25/4`

Take the square root of both sides

`rarrsqrt(x^2)=sqrt(25/4`

`rarrx=sqrt(25/4)`

Remember that,if we take the square root of a number,it can be positive or negative

So,

`rarrx=+-sqrt(25/4)`

Use the property

`color(brown)(sqrt(x/y)=sqrtx/sqrty`

`rarrx=+-sqrt25/sqrt4`

`color(blue)(rArrx=+-5/2`

Remember that the symbol `+-` means Plus or Minus

it indicates that

`rArrcolor(blue)(x=5/2,-5/2`