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The quadratic formula is:

Wondering how we got these formulas? 
Look at this!!!

The general form of a quadratic equation is:


Divide through by A

By completing the square

Add the square half of the coefficient of x to both sides.

Solving the right-hand side

$(x^2+\frac{Bx}{A}+\frac{B^2}{4A^2})$ is  $(x+\frac{b}{2A})^2$.


Taking the square root of both sides



For the sake of simplicity, 

Let's re-arrange the equation so that $x$ will be on one side while another variable will be placed on the other side.

If you're still confused about how we came up with the quadratic formula, check out my post on how to solve a quadratic equation by completing the square

Having proved the quadratic equation, let's look at more realistic illustrations

Example 1
Solve $4x^2+15x+9=0$ using the quadratic formula.

Here $A=4$, $B=15$, $C=9$
Remember that $x=\frac{-B\pm\sqrt{B^2-4AC}}{2A}$
$x=\frac{-15-9}{8}$ or $\frac{-15+9}{8}$
$x=\frac{-24}{8}$ or $\frac{-6}{8}$
$x=-3$ or $-0.75$

Example 2
Using the quadratic formula, solve $12x^2+11x+2=0$

Here, $A=12$, $B=11$, $C=2$
$x=\frac{-11+5}{24}$ or $\frac{-11-5}{24}$
$x=\frac{-1}{4}$ or $\frac{-2}{3}$
$x=-0.25$ or $-0.67$

Example 3
Compute $9x^2+3x-2=0$ using the quadratic formula

$A=9$, $B=3$, $C=-2$
$x=\frac{-3+9}{18}$ or $\frac{-3-9}{18}$
$x=\frac{1}{3}$ or $\frac{-2}{3}$
$x=0.333$ or $-0.667$

Example 4
Solve $3x^2-5x-2=0$ using the quadratic formula

Here $A=3$, $B=-5$, $C=-2$
Splitting the $\pm$
$x=\frac{5+7}{6}$ or $\frac{5-7}{6}$
$x=2$ or $-0.333$

The quadratic formula has been used to solve quadratic equations. 

If you're having trouble understanding this, I recommend going over it again.

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