ok im stuck on math, somebody help!!!!!?

Question

the problem is: t squared+3t=40: directions: solve each equation by completeing the square. Round to the nearest tenth.

Answer 1

t^2+3t-40=0
t^2 + 2* 3/2 t + (3/2)^2 -40 -(3/2)^2 =0
(t+3/2)^2 -169/4 =0
(t+3/2)^2 -(13/2)^2 =0
using formula a^2 - b^2= (a-b)(a+b) we get

(t+3/2-13/2)(t+3/2+13/2)=0
(t-5)(t+8)=0

==> t-5=0 or/and t+8=0
==> t=+5 or/and t= - 8

Answer 2

To have the form (t plus something)squared and end up with "3t" on the left, the factored equation must be: (t+1½) * (t+1½) = 40 + something. If so, the squared left side must be t-squared + 3t + 2¼, in other words, you add 2¼ to it so it must be 40 + 2¼ on the right side as well (=42¼): t-squared + 3t + 2¼ = 42¼.

Then, take the square root of each side to get: t+1½ = square root of 42¼ and solve for: t = square root of 42¼ – 1½ which equals 5. (Because 42¼ = 6½ squared and 6½ - 1½ = 5).

Stated as rounded to the nearest tenth (gotta watch those clever teachers!) the answer would be "5.0", not just "5"...To have the form (t plus something)squared and end up with "3t" on the left, the factored equation must be: (t+1½) * (t+1½) = 40 + something. If so, the squared left side must be t-squared + 3t + 2¼, in other words, you add 2¼ to it so it must be 40 + 2¼ on the right side as well (=42¼): t-squared + 3t + 2¼ = 42¼.

Then, take the square root of each side to get: t+1½ = square root of 42¼ and solve for: t = square root of 42¼ – 1½ which equals 5. (Because 42¼ = 6½ squared and 6½ - 1½ = 5).

Stated as rounded to the nearest tenth (gotta watch those clever teachers!) the answer would be "5.0", not just "5"...

Added:

I see there are many answers with different results. First, feed the answer in and check them:

t-squared + 3t = 40

t-squared = 5 squared = 25
3t = 3 * 5 = 15

So, 25 + 15 = 40? Yep.

Secondly, if you know the quadratic equation, you can see a second answer that works: –8.0. However, remember those clever teachers! The problem asks you to do it in a definite way and that way only yields the 5.0 answer, not both. Well, approached formally it does... but those clever teachers wouldn't want that would they? Just the most obvious answer?

Answer 3

t^2 + 3t = 40

Your first step is to take "half squared" of the coefficient of t. This is the key value to completing the square. By "half squared", you would first take half of that value, and then square the result.

In this case, the coefficient of t is 3. Half of 3 is 3/2, and squared is 9/4.

We have to add 9/4 to both sides, giving us

t^2 + 3t + 9/4 = 40 + 9/4

And now, the three terms on the left form a perfect square, and can be expressed as

(t + 3/2)^2 = 40 + 9/4

We can put the numbers on the right hand side under a common denominator and merge them into one.

(t + 3/2)^2 = 160/4 + 9/4
(t + 3/2)^2 = 169/4

Now, we take the square root of both sides. Note that whenever we take the square root of both sides of an equation, we HAVE to add "plus or minus" on the right hand side.

t + 3/2 = +/- sqrt(169/4)

To take the square root of a fraction, we can take the square root of both numerator and denominator. They happen to both be perfect squares (169 is 13^2 and 4 is 2^2), so we can effectively solve it

t + 3/2 = +/- 13/2

And now we move the 3/2 to the right hand side, giving us

t = 3/2 +/- 13/2

-or-

t = [3 +/- 13]/2

This gives us two values for t:
t = (3 + 13)/2
t = (3 - 13)/2

Therefore, t = 15/2, -10/2
or t = 15/2, -5

Answer 4

upload the two numbers mutually, then multiply the sum by employing technique of the 1st style of the situation..... 2+3 = 5 x 2 = 10 (2+ 3 = 5, now take 5 and multiply it by employing technique of two) 7+2 = 9 x 7 = sixty 3 6+5 = 11 x 6 = 66 8+4 = 12 x 8 = ninety six 9+7 = sixteen x 9 = a hundred 40 4

Answer 5

2.5