# maths

(400t-300)(400t-300)+(200t-100)(200t-100)
complete the square showing all steps

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1. (400t-300)(400t-300)+(200t-100)(200t-100)=

(400t-300)^2+(200t-100)^2=

(400^2*^2-2*400t*300+300^2)+(200^2*t^2-2*200t*100+100^2)=

160.000t^2-240.000t+90.000+40.000t^2-40.000t+10.000=

200.000t^2-280.000t+100.000

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2. no worry found the solution to be 200000((t-7/10)^2+1/100)
first by multiplying out as above to get 200000t^2-280000t+100000
then taking out the factor of 200000 to get
200000(t^2-7/5t+1/2)
then using the formula
x^2+2px=(x+p)^2-p^2
to get
200000((t-7/10)^2-49/100+1/2)
simplifying gives
200000((t-7/10)^2+1/100)
thankyou for all the help from the people that toke the time to answer and if anyone has got the time could you please check my answer for me.

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posted by simon

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