Question 151224
Here are two ways to solve this problem



Method #1 Quadratic Formula (preferred method):



{{{x^2-4x-60=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-4}}}, and {{{c=-60}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(-4) +- sqrt( (-4)^2-4(1)(-60) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-4}}}, and {{{c=-60}}}



{{{x = (4 +- sqrt( (-4)^2-4(1)(-60) ))/(2(1))}}} Negate {{{-4}}} to get {{{4}}}. 



{{{x = (4 +- sqrt( 16-4(1)(-60) ))/(2(1))}}} Square {{{-4}}} to get {{{16}}}. 



{{{x = (4 +- sqrt( 16--240 ))/(2(1))}}} Multiply {{{4(1)(-60)}}} to get {{{-240}}}



{{{x = (4 +- sqrt( 16+240 ))/(2(1))}}} Rewrite {{{sqrt(16--240)}}} as {{{sqrt(16+240)}}}



{{{x = (4 +- sqrt( 256 ))/(2(1))}}} Add {{{16}}} to {{{240}}} to get {{{256}}}



{{{x = (4 +- sqrt( 256 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (4 +- 16)/(2)}}} Take the square root of {{{256}}} to get {{{16}}}. 



{{{x = (4 + 16)/(2)}}} or {{{x = (4 - 16)/(2)}}} Break up the expression. 



{{{x = (20)/(2)}}} or {{{x =  (-12)/(2)}}} Combine like terms. 



{{{x = 10}}} or {{{x = -6}}} Simplify. 



So our answers are {{{x = 10}}} or {{{x = -6}}} 


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Method #2 Factoring:


{{{x^2-4x-60=0}}} Start with the given equation


{{{(x-10)(x+6)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x-10=0}}} or  {{{x+6=0}}} 


{{{x=10}}} or  {{{x=-6}}}    Now solve for x in each case



So our answers are 


 {{{x=10}}} or  {{{x=-6}}} 



Notice if we graph {{{y=x^2-4x-60}}}  we can see that the roots are {{{x=10}}} and  {{{x=-6}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,12,-10,10,0, x^2-4x-60) }}}




Note: even though the factoring method may seem easier, it does not work for every quadratic.