x^2 + 49 =-14x solve?

Question

I'm more interested in the steps to find the answer than the answer itself. Can someone pls spell this out for me? Thanks =)

Answer 1

ok

This is a quadratic equation (because x² is present and there is no higher power than a square in this equation).

We solve quadratic equations by taking everything to the left hand side:

x² + 14x + 49 = 0

Then we factorize this in to two factors (x-a)(x-b) such that a+b = 14 and a·b = 49

(x+7)(x+7) = 0
or
(x+7)² = 0

The solution to this equation is
x = - 7,
because (-7+7)² = 0² = 0

__________

If you are not in the mood to factorize, you can also use the quadratic formula.
The solutions of a quadratic equation
Ax² + Bx + C = 0
can be found with the quadratic formula:
x = [ -B ± √(B² - 4AC) ] / [2A] .

In your case the coefficients are:
A = 1, B =14, C = 49

Plug them in the quadratic formula:
x = [ -14 ± √(14² - 4·1·49) ] / [2·1]
x = [ -14 ± √0 ] / 2
x = -14 / 2
x = -7

Hope this helps.

Answer 2

first, add 14x to both sides. you get x^2 +14x+49=0
Then find the discriminant using d= b^2-4ac d=14^2-4(49)
d=196-196=0 This means that the equation is factorable and has one double root (answer). TO factor, multiply a by c (1 and 49) and try to find two numbers that multiply to ac (49) and add up to b (14). They can be negative. In this case though the numbers are clearly 7 and 7. x^2+7x+7x+49=0
Now factor by grouping. To factor by grouping, take the first two terms and find what common. Then do the same for the second group of terms. x(x+7)+7(x+7)=o
Then, pull out the x=7. (In this case, though, x^2+14x+49=0 was a square polynomial, which could have been recognized from the start by taking half of b and squaring it to see if it equals b, if it does (which in this case it would), it is a square polynomial.) (x+7)^2=0 Now take the square root of both sides. x+7=0 X=-7

Answer 3

x^2 + 49 = -14x
The above equation can be written as x^2 + 14x + 49 = 0
The next step is splitting +14x into +7x and +7x when multiplied gives +49 x^2 which should be same when the first term and the last term are multiplied which gives the result as +49x^2..
Hence the equation becomes x^2 + 7x + 7x + 49 = 0
Factorizing the above equation,
x(x + 7) + 7(x + 7) = 0
This can be written as (x + 7) (x + 7) = 0 which can be written as (x + 7)^2. x = -7 is the answer.

Answer 4

1. you subtract the -14x to the other side 1x^2 + 14x + 49
2. then your have to factor it by multiplying (1*49) which is 49, and you have to get two number that will multiply together to get 49, but the numbers will also add up to 14.
3. the two numbers are 7 and 7 because 7*7=49 and 7+7=14
4. now your equation looks like this x^2 + 7x + 7x + 49
5. now you put them together like this (x^2 + 7x) (7x+49)
6. then factor it by taking an "x" out of the first one and a "7" out of the second one... x( x+ 7) 7(x + 7)
7. now you combine the two so it's (x +7) (x+ 7)
8. you can also write the answer as (x + 7)^2 =0
9. since it is a quadratic equation you have to find what x equals and in this case.. x=-7


hope this helps

Answer 5

Okay, so first add -14x to both sides so that you get a quadratic equation equal to zero: x^2 + 14x + 49=0
Then solve for x by finding two numbers that add up to 14 and multiply up to 49:
7 + 7 = 14
7 x 7 = 49

So you get (x+7)(x+7)=0
Or (x+7)^2 = 0

Answer 6

Add 14x to both sides:
x²+14x+49=0.
The discriminant of this equation is 14²-4(49) = 0.
That means the left-hand side is a square.
Factoring, we get
(x+7)(x+7) = 0,
so your equation has a double root at -7.

Answer 7

move the -14x to the other side and you will end up with

x^2 + 14 x +49=0


then find two numbers that add up to give 14 and muliply to give 49 so in this case it is 7

so you will end up with x^2+7x+7x+ 49=0 factor it

(x+7)(x+7)=0

answer will be x=-7

Answer 8

First move -14x to the left side... changing the sign...
you get
x^2+14x+49=0

then you factor
it's a perfect square equation...
you use 7 as the factor...

you get (x+7)(x+7)=0
or (x+7)^2=0

x+7 has to equal zero... so x=-7

Answer 9

Add 14x to both side to make your equation equal to 0:

x² + 14x + 49 = 0

Factor:
(x+7)(x+7) = 0

Set factor(s) equal to 0:

x+7 = 0 ---> x = -7

Answer 10

x^2 + 14x + 49 = 0

(x + _ ) (x + _)

7 X 7 = 49, so try 7 -

(x + 7) (x + 7) = 0 --> so,

(x + 7) = 0, x = -7