1. derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
2. divide all terms in the equation by a.
3. subtract the constant (the term without an x) from both sides.
4. add a constant (in terms of a and b) that will complete the square.
5. take the square root of both sides of the equation.
6. solve for x.

We are given that:

a x^2 + b x + c = 0

Divide all terms with c/ a:

x^2 + (b / a) x + (c / a) = 0

Subtract c from both sides:

x^2 + (b / a) x + (c / a) – c / a = 0 – c / a

x^2 + (b / a) x = - c / a

Add a constant k to complete the square:

where k = ((b / a) / 2)^2 = (b /2a)^2

x^2 + (b / a) x  + k = - c / a + k

x^2 + (b / a) x + (b/2a)^2 = - c / a + (b /2a)^2

So the perfect square trinomial is:

(x + b/2a)^2 = - c / a + (b /2a)^2

Taking the square root of both sides:

x + b/2a = sqrt [- c / a + (b /2a)^2]

x = sqrt [(-c/a) + (b /2a)^2] – (b/2a)

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step-by-step explanation: