Respuesta :

boffeemadrid

Answer:

Step-by-step explanation:

Consider the quadratic equation, we have

[tex]ax^2+bx+c=0[/tex]

Dividing the equation by a, we get

[tex]x^2+\frac{b}{a}x+\frac{c}{a}=0[/tex]

Put [tex]\frac{c}{a}[/tex] on the other side,

[tex]x^2+\frac{b}{a}x=\frac{-c}{a}[/tex]

Add [tex](\frac{b}{2a})^2[/tex] on both the sides,

[tex]x^2+\frac{b}{a}x+(\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2[/tex]

completing the square, we have

[tex](x+\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2[/tex]

Now, solving for x,

[tex]x+\frac{b}{2a}={\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}[/tex]

[tex]x=\frac{-b}{2a}{\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}[/tex]

Multiply right side by [tex]\frac{2a}{2a}[/tex],

[tex]x=\frac{-b{\pm}\sqrt{b^2-4ac}}{2a}[/tex]

which is the required quadratic formula.

pstnonsonjoku

The general form of a quadratic equation is obtained from the completing the square method as x = -b ±√b^2 - 4ac/2a.

General form of a quadratic equation;

A quadratic equation is of the sort; ax^2 +bx +c =0. Now we have to apply the completing the square method;

Dividing through by a we have;

x^2 + b/ax +c/a = 0

Now we have to move c/a to the other side;

x^2 + b/ax  = -c/a

If we add half of b/a to both sides;

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

(x +b/2a)^2 = b^2/4a^2 -c/a

x +b/2a = √ b^2/4a^2 -c/a

x = -b ±√b^2 - 4ac/2a

Learn more about quadratic equation: https://brainly.com/question/15167411