(400t-300)(400t-300)+(200t-100)(200t-100)
complete the square showing all steps
(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
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.
To complete the square for the expression (400t-300)(400t-300)+(200t-100)(200t-100), we can follow these steps:
Step 1: Expand the expression using the distributive property:
(400t-300)(400t-300) + (200t-100)(200t-100)
= (400t)(400t) - (400t)(300) - (300)(400t) + (300)(300) + (200t)(200t) - (200t)(100) - (100)(200t) + (100)(100)
Step 2: Simplify the expression by combining like terms:
= 160000t^2 - 120000t - 120000t + 90000 + 40000t^2 - 20000t - 20000t + 10000
Step 3: Combine like terms:
= 200000t^2 - 440000t + 10000
Step 4: Group the terms to complete the square:
= (200000t^2 - 440000t) + 10000
Step 5: Factor out the coefficient of t^2 from the first two terms:
= 200000(t^2 - 2.2t) + 10000
Step 6: To complete the square, take half of the coefficient of t (-2.2), square it, and add it as a constant term inside the parentheses. Half of -2.2 is -1.1, squared is 1.21:
= 200000(t^2 - 2.2t + 1.21 - 1.21) + 10000
Step 7: Rewrite the expression inside the parentheses as a perfect square:
= 200000((t - 1.1)^2 - 1.21) + 10000
Step 8: Distribute the 200000 to both terms inside the parentheses:
= 200000(t - 1.1)^2 - 200000(1.21) + 10000
Step 9: Simplify the expression by multiplying and combining like terms:
= 200000(t - 1.1)^2 - 242000 + 10000
Step 10: Combine like terms:
= 200000(t - 1.1)^2 - 232000
Therefore, the completed square form of the expression (400t-300)(400t-300)+(200t-100)(200t-100) is 200000(t - 1.1)^2 - 232000.