Question 115480
I'll do the first few to give you an idea how to do these


#1


{{{x^2+7x=8}}} Start with the given equation



{{{x^2+7x-8=0}}} Move all of the terms to the left side



{{{(x+8)(x-1)=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+8=0}}} or  {{{x-1=0}}} 


{{{x=-8}}} or  {{{x=1}}}    Now solve for x in each case



So our answer is 

 {{{x=-8}}} or  {{{x=1}}} 



Notice if we graph {{{y=x^2+7x-8}}} we can see that the roots are {{{x=-8}}} and  {{{x=1}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2+7x-8) }}}



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#2


{{{x^2=25}}} Start with the given equation



{{{x^2-25=0}}} Move all of the terms to the left side



{{{(x+5)(x-5)=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+5=0}}} or  {{{x-5=0}}} 


{{{x=-5}}} or  {{{x=5}}}    Now solve for x in each case



So our answer is 

 {{{x=-5}}} or  {{{x=5}}} 



Notice if we graph {{{y=x^2-25}}} we can see that the roots are {{{x=-5}}} and  {{{x=5}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2-25) }}}


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#3



{{{2t^2+8t-64=0}}} Start with the given equation



{{{2(t^2+4t-32)=0}}} Factor out the GCF 2


{{{2(t+8)(t-4)=0}}} Factor the inner expression (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:

{{{t+8=0}}} or  {{{t-4=0}}} 


{{{t=-8}}} or  {{{t=4}}}    Now solve for t in each case



So our answer is 

 {{{t=-8}}} or  {{{t=4}}} 



Notice if we graph {{{y=2t^2+8t-64}}} we can see that the roots are {{{t=-8}}} and  {{{t=4}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, 2x^2+8x-64) }}}