Could you please explain how are these the answers?Its about solving polynomials?

Question

1) 6t+t squared=0 the book says the answer is Negative 2
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3
2)0=25+x squared +10x the answer is Negative 5

Answer 1

reassembling the equations...
1. t(t+6)=0 so t=-6, 0
2. 0=(5+x)squared so x+5=0 so x=-5
sry when i posted it 10 sec ago i read it wrong

Answer 2

Answer 1:
t^2 + 6t = 0
t(t + 6) = 0

Either t = 0
or t + 6 = 0

If t + 6 = 0, t = -6

t = 0, -6 is the solution

Answer 2:
x^2 + 10 + 25 = 0
(x)^2 + 2(5)x + (5)^2 = 0
(x + 5)(x + 5) = 0

x + 5 = 0
x = -5


The book lists the first answer wrong. There is no way a quadratic equation that is not a perfect square can have only one solution.
There is a very easy way of checking if a quadratic expression is a perfect square.

Quadratics are expressed as ax^2 + bx + c

The quadratic is a perfect square is b^2 - 4ac = 0

b^2 - 4ac is called the discriminant.

Answer 3

You need to get your expressions more easy to follow. Use ^2 to indicate squared.
In #1 t^2 + 6t = 0, or t(t+6)=0. Then t=0 or -6
In #2 x^2+10x+25 is a "perfect square" since 25 is a perfect square and 2 x sqrt(25) = 10. Then
(x+5)^2 =0, giving a twin root of -5.

Answer 4

when working with polynomials you arrange the terms so they decend away from the = sign. so for problem 2(two) you would rewrite it like this:

0=Xsquared+10x+25

then use F.O.I.L. (first, outside, inside, last) to further factor this down...you will get:

0=(x+5)(x+5)

in order for (x+5) to equal zero you would make x= -5.

Check by switching the -5 in for X:

0=(-5+5)(-5+5)

when x= -5 it will satisfy the equation and equal 0.

As for the first question:

0=Tsquared + 6T
0=T(T+6)

and thats as far as i can take that one. its been a while since i haved covered this stuff. I can't see how negative two-thirds could be the answer from this step. I know if you plug negative two-thirds into the orginal problem it works, but the trouble is how are you supposed to get that answer, sorry i can't be more help on the first one.

Answer 5

answer for second question

x(square)+10x+25=0
splitting the middle term
x^2+5x+5x+25=0
x(x+5)+5(x+5)=0
(x+5)(x+5)=0
answer is x = -5

sorry i could not crack the first question

Answer 6

6 (-2/3) + (-2/3)^2=0
-4 + 4=0


the second answer is the same way...
0=25+x^2+10X
0=25+(-5)^2+10(-5)
0=25+(25)+(-50)
0=25+25-50
0=50-50
0=0

Answer 7

a million. 9x^2 = 4 9x^2 - 4 = 0 (component out) (3x + 2) (3x - 2) = 0 3x + 2 = 0 ; 3x - 2 = 0 3x = -2 ; 3x = 2 x = -2/3 ; x = 2/3 2. x^2 - 2x = 18 + 5x x^2 - 2x - 5x - 18 = 0 x^2 - 7x - 18 = 0 (x -9) (x + 2) = 0 x - 9 = 0 ; x + 2 = 0 x = 9 ; x = -2

Answer 8

6t+6 = 7t so you have 7t^2=0 => 49t^2 = 0 therefore:

t should be equal to 0.

And I'm sorry I can't figure out what you mean by the second question.

Answer 9

well the first one is noe clear to me1
but the 2nd problem is simple!
Xsquare+10X+25=(X+5)square=0
gives X= -5!!

Answer 10

6t + t*t = 0 (subtract -6t from both sides)
t*t = -6t (divided both side by t)

t = -6

check the answer
6(-6) + (-6)(-6) = 0