I am in desperate need of a math genius to show me how to do this quadratic?

Question

here is the question x^2-10x+16=0
find the quadratic by completing the square.

can you please give me the steps to get the answer I have a test tomorrow. Thank you:)

Where does the 2 come from that I divide by 10?

Answer 1

x^2 - 10x + 16 = 0 First thing you want to do is group the x terms in ( ) and put the 16 outside... like so...
(x^2 - 10x + ____) + 16 = 0 Now completing the square means complelying ( ) bascally finding what number fills the black... in order to do this take the b value in this case it would be 10 and divide it by 2 in our cause that would give us 5 and then square the answer... 25 that is the number that goes in the blank... so we have...
(x^2 - 10x + 25) + 16 = 0 But since we added 25 to the equation to keep the equation equal to what it was before we also must subtract 25. So we get...
(x^2 - 10x + 25) + 16 - 25 = 0 which equals
(x^2 - 10x + 25) -9 = 0 Now it is easy to factor what's in ( ) we get...
[(x - 5)^2] - 9 = 0 This is your answer
---------------------------------------------
But now if you want to solve for x then...
[(x - 5)^2] - 9 = 0 add 9 to both sides...
(x - 5)^2 = 9 which equals
(x - 5)(x - 5) = 9
(x - 5) = 9 add 5 to both sides
x = 14 and you get 14 twice. Which means if you were to graph it x = 14 would be a double root.

If you need further help or clarification email me or im me. Good Luck.

Answer 2

Completing the square means that you create a quadratic equation that is a trinomial square. To create a trinomial square from that equation, first you must get the constant to the other side
x^2 -10x +16=0
x^2 -10x=-16
from there, you divide the x coefficient in half and sqaure it.
the x coeffient of x^2 -10x=-16 is -10
-10/2=5
5^2=25
from there you take 25 and add it to both sides, since the constant and the x^2 coeffient must be positive for it to be a trinomial square
x^2 -10x+25=-16+25
x^2 -10x+25=9
now you factor out the trinomial square
(x-5)(x-5)=9
take the square root of both sides
the square root of x-5 squared is obviously x-5
x-5=3 or -3
remember that there is always two roots for all positive numbers
now it becomes two separate problems
x-5=3 or x-5= -3
x=3+5 or x= -3+5
x=8 or x=2
there are your answers

Answer 3

Let me sketch the solution:

The cube divides the ladder in two parts, which I will take to have
lengths 5+x and 5-x, and I will try to solve for x (computation of the
height you are looking for is straightforward then.) I chose this use
of x because of the symmetry. If x is a solution, then of course -x is
also a solution. We have the following picture:

|
|\
| \
| \5+x
t| \
| \
|__3__\
| |\
3| 3| \5-x
|_____|__\___
3 u

We know with help of the Pythagorean theorem:

u^2 = (5-x)^2 - 9 = x^2 - 10x + 16
t^2 = (5+x)^2 - 9 = x^2 + 10x + 16

The slopes of the two parts of the ladder must of course be equal, so
the following must be true:

t/3 = 3/u
tu = 9
t^2*u^2 = 81
(x^2-10x+16)*(x^2+10x+16) = 81
x^4 - 68x^2 + 175 = 0

This equation is quadratic in x^2, and you can find four solutions for
x. But not all solutions are valid. Of course 5-x as well as 5+x must
be greater than 3, so you must have -2 < x < 2. In fact there are two
solutions left, as you already said.

If you need more help, just write back.

Answer 4

The quadratic formulation is effortless to apply, quite. that's as follows: x = (-b +- ?(b^2 - 4ac))/2a purely plug interior the coefficients out of your quadratic equation (those numbers in front of something that multiply by using x) a, b, and c respectively. i'm going to exhibit by using fixing concern a million: a^2 - 5a + 6 = 0 . . . . . . . . . . . . . the unique equation, in its acceptable form x = (5 +- ?(25 - 4 * a million * 6)/(2 * a million) . . . i've got purely taken the quadratic formulation from above, and plugged on your coefficients: a = a million (no coefficient shown, so that's a million); b = 5; c = 6) x = (5 +- ?(25 - 24)/(2) . . . . . . . . .purely the undemanding multiplication finished x = (5 +- ?a million)/2 . . . . . . . . . . . . . . undemanding subtraction finished x = (5 +- a million)/2 . . . . . . . . . . . . . . . The sq. root of a million is a million x = (5 + a million)/2 or (5 - a million)/2 . . . . . . . The quadratic formulation provides us 2 means solutions, the two -b plus or minus the discriminant (sq. root of b squared - 4ac) x = 6/2 or 4/2 . . . . . . . . . . . . . . undemanding subtraction finished x = 3 or 2 . . . . . . . . . . . . . . . . . undemanding branch finished As you will locate, there are 2 accessible solutions, while utilising the quadratic formulation. I advise you memorize the quadratic formulation, as that's significant in undemanding algebra, and you will finally end up utilising it lots. try determining something of those issues from what i've got advised you.

Answer 5

you know you need something multiplied by something that equals to 16 so the options are 1 and 16 or -1 and -16 or 2 and 8 or -2 and -8 or 4 and 4 or -4 and -4

but they also need to add to -10 which means -2 and -8

therefore
(x-2)(x-8) = x^2 - 10x + 16 = 0

so if (x-2)(x-8) = 0
then (x-2)0 = 0 or 0(x-8) =0
so
x-2 = 0 therefore x = 2
x-8 = 0 therefore x = 8
x=2, x=8

Answer 6

quadratics are in the form

ax^2 + bx + c = 0

When the a position = 1 , as in your example
then

look at the c position, + 16 in your case
and at the b position, - 10

You need two numbers which multiply together = + 16
and the same two numbers added together = - 10

-2(-8) = + 16
-2 - 8 = -10

so

(x - 2)(x - 8) = 0

so

x = 2 , or 8 as your solution

Answer 7

divide the -10 by 2 to get: (x-5)^2 but -5 squared is 25, so you need to subtract 9 to get the 19: (x-5)^2-9 is the answer.

Answer 8

x^2-10x+16=0
x^2-10x+25-25+16=0
(x-5)^2-9=0
(x-5)^2=9
x-5=±3
x=5+3=8
x=5-3=2
roots are 2 & 8

Answer 9

x^2-10x=-16
x^2-10x+25=-16+25
(x-5)^2=9