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

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Answer 1 · 2016-03-30T11:55:02

$x=3,2$

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

Rewrite in standard form

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

This is a Quadratic equation (in form $ax^2+bx+c=0$ )

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

Remember that $a,bandc$ are the coefficients of $x^2,xand6$

Now,

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

$rarrx=(-(-5)+-sqrt(-5^2-4(1)(6)))/(2(1))$

$rarrx=(5+-sqrt(-5^2-4(1)(6)))/(2)$

$rarrx=(5+-sqrt(25-4(1)(6)))/(2)$

$rarrx=(5+-sqrt(25-(24)))/(2)$

$rarrx=(5+-sqrt(1))/(2)$

$rarrx=(5+-1)/(2)$

Now we have $2$ solutions for $x$

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

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

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

How do you solve 0 = x^2 - 5x + 60 = x^2 - 5x + 6 using the quadratic formula?