# How do you solve 0 = x^2 - 5x + 6 using the quadratic formula?

Mar 30, 2016

$x = 3 , 2$

#### Explanation:

color(blue)(0=x^2-5x+6

Rewrite in standard form

rarrcolor(purple)(x^2-5x+6=0

This is a Quadratic equation (in form $a {x}^{2} + b x + c = 0$)

color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)

Remember that $a , b \mathmr{and} c$ are the coefficients of ${x}^{2} , x \mathmr{and} 6$

Now,

color(red)(a=1,b=-5,c=6

$\rightarrow x = \frac{- \left(- 5\right) \pm \sqrt{- {5}^{2} - 4 \left(1\right) \left(6\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{5 \pm \sqrt{- {5}^{2} - 4 \left(1\right) \left(6\right)}}{2}$

$\rightarrow x = \frac{5 \pm \sqrt{25 - 4 \left(1\right) \left(6\right)}}{2}$

$\rightarrow x = \frac{5 \pm \sqrt{25 - \left(24\right)}}{2}$

$\rightarrow x = \frac{5 \pm \sqrt{1}}{2}$

$\rightarrow x = \frac{5 \pm 1}{2}$

Now we have $2$ solutions for $x$

color(purple)(x=(5+1)/(2)=6/2=3

color(orange)(x=(5-1)/(2)=4/2=2

color(blue)( :.ul bar| x=2,3|
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