Question

Please help!!!!!

Answer 1

Answer:

Step-by-step explanation:

Consider the quadratic equation, we have

$ax^2+bx+c=0$

Dividing the equation by a, we get

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

Put $\frac{c}{a}$ on the other side,

$x^2+\frac{b}{a}x=\frac{-c}{a}$

Add $(\frac{b}{2a})^2$ on both the sides,

$x^2+\frac{b}{a}x+(\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2$

completing the square, we have

$(x+\frac{b}{2a})^2=\frac{-c}{a}+(\frac{b}{2a})^2$

Now, solving for x,

$x+\frac{b}{2a}={\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}$

$x=\frac{-b}{2a}{\pm}\sqrt{\frac{-c}{a}+(\frac{b}{2a})^2}$

Multiply right side by $\frac{2a}{2a}$,

$x=\frac{-b{\pm}\sqrt{b^2-4ac}}{2a}$

which is the required quadratic formula.

Answer 2

Finish square of ax2 + bx + c = 0 to get the Quadratic Formula. Then youDivide both sides of the equation by A, so the coefficient of x2 is 1. Write again so the left side is in form x2 + bx.