Respuesta :
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)
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: