The principle of square roots requires that the square root of the side with the unknown (x) only includes x without any exponent (other than 1).

The simplest form that fits this criterion is:

**x**^{2} = k

**x = +/- sqrt(k)**

but x can also be an expression. For quadratic equations, the **standard form** can

be used like this:

**a(x-h)**^{2} + k = 0

**(x-h)**^{2} = -k/a

Now you can take the square root of both sides and solve for x:

**x-h = +/- sqrt(-k/a)**

**x = h +/- sqrt(-k/a)**

Note that in order to get real numbers as answers, **a** and **
k** must have opposite signs so that **-k/a** is positive.

An equation in the **general form** can be converted to the **
standard form**:

**ax**^{2} + bx + c = 0

becomes

**a(x-h)**^{2} + k = 0

**(x-h)**^{2} = -k/a

where:

**a = a, h = b/2a, k = c/a - (b/2a)**^{2}

(This conversion uses "completing the square".)

It is usually easier to solve a general form equation using the more familiar factoring or the quadratic

formula.

I Hope this helps.

Gene G.