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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.

Respuesta :

barnuts

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)

generictracermain

Answer:

My equation is 3x^2 + 12x + 24 = 0. When I divide all of the terms by 3, the equation becomes x^2 + 4x + 8 = 0. When I subtract both sides by the constant, 8, the equation is x^2 + 4x = -8. When I add a constant to create the perfect square, the equation now becomes x^2 + 12x + 36 = 28. Finally, the equation simplified equals (x + 6)= the square root of 28.

Step-by-step explanation:

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