SOLUTION: Please help me solve these problem. t^2-2t=15 0.9a^2+5.4a-4=0 x^2+10x+c Find C Thank You So Much!

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Question 197874: Please help me solve these problem.
t^2-2t=15
0.9a^2+5.4a-4=0
x^2+10x+c
Find C
Thank You So Much!
Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



t%5E2-2t=15 Start with the given equation.


t%5E2-2t-15=0 Get all terms to the left side.


Notice we have a quadratic in the form of At%5E2%2BBt%2BC where A=1, B=-2, and C=-15


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-15%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-2, and C=-15


t+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-15%29+%29%29%2F%282%281%29%29 Negate -2 to get 2.


t+=+%282+%2B-+sqrt%28+4-4%281%29%28-15%29+%29%29%2F%282%281%29%29 Square -2 to get 4.


t+=+%282+%2B-+sqrt%28+4--60+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-15%29 to get -60


t+=+%282+%2B-+sqrt%28+4%2B60+%29%29%2F%282%281%29%29 Rewrite sqrt%284--60%29 as sqrt%284%2B60%29


t+=+%282+%2B-+sqrt%28+64+%29%29%2F%282%281%29%29 Add 4 to 60 to get 64


t+=+%282+%2B-+sqrt%28+64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%282+%2B-+8%29%2F%282%29 Take the square root of 64 to get 8.


t+=+%282+%2B+8%29%2F%282%29 or t+=+%282+-+8%29%2F%282%29 Break up the expression.


t+=+%2810%29%2F%282%29 or t+=++%28-6%29%2F%282%29 Combine like terms.


t+=+5 or t+=+-3 Simplify.


So the solutions are t+=+5 or t+=+-3



# 2

0.9a%5E2%2B5.4a-4=0 Start with the given equation.


9a%5E2%2B54a-40=0 Multiply EVERY term by 10 to make every number a whole number.


Notice we have a quadratic in the form of Aa%5E2%2BBa%2BC where A=9, B=54, and C=-40


Let's use the quadratic formula to solve for "a":


a+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


a+=+%28-%2854%29+%2B-+sqrt%28+%2854%29%5E2-4%289%29%28-40%29+%29%29%2F%282%289%29%29 Plug in A=9, B=54, and C=-40


a+=+%28-54+%2B-+sqrt%28+2916-4%289%29%28-40%29+%29%29%2F%282%289%29%29 Square 54 to get 2916.


a+=+%28-54+%2B-+sqrt%28+2916--1440+%29%29%2F%282%289%29%29 Multiply 4%289%29%28-40%29 to get -1440


a+=+%28-54+%2B-+sqrt%28+2916%2B1440+%29%29%2F%282%289%29%29 Rewrite sqrt%282916--1440%29 as sqrt%282916%2B1440%29


a+=+%28-54+%2B-+sqrt%28+4356+%29%29%2F%282%289%29%29 Add 2916 to 1440 to get 4356


a+=+%28-54+%2B-+sqrt%28+4356+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


a+=+%28-54+%2B-+66%29%2F%2818%29 Take the square root of 4356 to get 66.


a+=+%28-54+%2B+66%29%2F%2818%29 or a+=+%28-54+-+66%29%2F%2818%29 Break up the expression.


a+=+%2812%29%2F%2818%29 or a+=++%28-120%29%2F%2818%29 Combine like terms.


a+=+2%2F3 or a+=+-20%2F3 Simplify.


So the solutions are a+=+2%2F3 or a+=+-20%2F3



# 3

Are you looking for the value of "c" that will make x%5E2%2B10x%2Bc a perfect square??? There are no other instructions?

If so, then take half of 10 to get 5. Square 5 to get 25. This means that c=25


So the expression is x%5E2%2B10x%2B25 which is a perfect square.