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Explain in your own words how the principle of square roots is used to solve quadratic equations.

What form must a quadratic equation be in to use the principle of square roots
for solving? Demonstrate the process using your own example or
solve the
quadratic equation x2 + 6x -16 = 0 by completing the
square. Explain how to solve a quadratic
example or solve the
quadratic equation x2 + 6x -16 = 0 by using the quadratic
formula.

Gene G. | You can do it! I'll show you how.You can do it! I'll show you how.
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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:
x2 = 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:

ax2 + 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.