homework help?

Question

two questions:solve for x: -3(x+5)+7x=25 also solve for x: xsquared+3x-54=0

Answer 1

Okay here we go -

#1. -3(x+5) + 7x = 25

first you should work out the first side with the brackets and addition

-3 (x+5) +7x = 25
-3x + -15 +7x = 25
-15 + 4x = 25

so now that you have that done you want x by itself on the left side. so what do you do? you have to get rid of the -15 on the left by adding 15 >> and when you do something to one side you must do the same for the other.

-15 + 4x + 15 = 25 + 15
4x = 40

so now that this is done you want x by itself so you have to divide the 4 from it and remember you have to do the same to both sides.

4x + 40
---- -----
4 4

x = 10

you can now check your answer to see if it is correct

-3 (10 + 5) + 7(10) = 25

-3 (15) + 70 = 25

-45 + 70 = 25

25 = 25


Now to the next question
x(sq) + 3 x - 54 = 0

first question for you have you do FOIL & reverse FOIL

when you have any equation like this you have to do the reverse foil

x(sq) + 3x - 54 = 0

so to do the reverse you should look at what you are aiming for
fo il fi ol
(a + b)(c + d) = 0
F - first
O - outside
I - inside
L - last

ac + ad +bd + bc

here is a short example of Foil and reverse Foil
(x + 2) (x - 2) = 0
x(sq) - 2x + 2x - 4 = 0
x(sq) - 4 = 0
x(sq) = 4
x = 2

reverse

x(sq) - 4 = 0

what are the multipules of -4?
1 4, -1 -4, 2 -2

what pair added together gives you 0?
2 -2

(x +2)(x-2) = 0

So in this equation

x(sq) + 3x - 54 = 0

what are the multipuls of -54 and which pair when added gives you 3

1 -54, -1 54, 2 -27, -2 27, 3 -18, -3 18, 6 -9, -6 9

the two when added that gives you 3 is
-6 and 9

so you would now write your equation like this

(x + 9) (x - 6) = 0

so how do you solve for x?

This is a process of elimanation. You know that anything multiplied by 0 equals 0 so one of the brackets when solved with the value of x must be 0

so the value of x is either -9 or 6 so it is now time to place these values in the orginal equation to see if it works

x(sq) + 3x - 54 = 0

-9(sq) + 3(-9) - 54 = 0
81 + -27 - 54 = 0
81 - 81 = 0

so -9 works

what about 6?

6(sq) + 3(6) - 54 = 0
36 + 18 - 54 = 0
54 - 54 = 0

so 6 works too

so the values of x are 6, -9

I hope this solves the questions for you

God Bless and Good Luck in math

Answer 2

- 3(x + 5) + 7 = 25

- 3x - 15 + 7 = 25

- 3x - 8 = 25

- 3x - 8 + 8 = 25 + 8

- 3x = 33

- 3x / - 3 = 33 / - 3

x = - 33/3

x = - 10

- - - - - - - -

x² + 3x - 54 = 0

First term x = 1

find the sum of the middle term. Multiply the first term 1 by the last term 54 = 54 and factor

Factors of 54 = 1 2 3 6 9 18 27 54

9 - 3 satisfy the sum of the middle term

insert 9x and - 3x into the equation

x² + 3x - 54 = 0

x² + 9x - 3x - 54 = 0

x(x + 9) - 3(x + 9)

(x - 3)(x + 9)

- - - - - -

Roots

x - 3 = 0

x - 3 + 3 = 0 + 3\

x = 3

- - - - - -

Roots

x + 9 = 0

x + 9 - 9 = 0 - 9

x = 9

- - - - - - - - -s-

Answer 3

1.) -3(x+5)+7x =25
Distribute 3 first.
-3x - 15 + 7x = 25
Add or subtract like numbers.
4x -15 = 25
4x = 25 + 15
4x = 40
x = 10
2.) x^2 + 3x -54 = 0
Find the factors of -54 that add up to 3.
They are: -9 *6.
Now expand the equation like this:
x^2 - 9x + 6x - 54
(we are not changing the equation here since -9x + 6x = 3x.)
now, separate the equation like this:
(x^2-9x)+(6x-54) = 0
take out the common factors.
x(x-9) + 6(x-9) = 0
(x+6)(x-9) = 0
One of the factors must be 0 in order for the product to be 0.
So first let (x+6) be 0.
so, x+6 = 0
x = -6
Next let (x-9) be 0
so, x-9 = 0
x = 9
Therefore, x has two answers.
x = -6 or 9

Answer 4

1) first open the bracket

it becomes: -3x-15+7x = 25

therefore, 4x-15 = 25 or 4x = 40

i.e. x = 40/4 = 10.

2) x^2 + 3x -54 = 0

I think this problem is incomplete as I have seen these problems with square only with two equations at least.

otherwise your answer should be

x^2 + 3x = 54
3x = 54 - x^2
x = (54 - x^2)/3 this is the value of x.

Answer 5

1. First, distribute: -3x - 15 + 7x = 25.

Then combine like terms: 7x - 3x - 15 = 25, i.e. 4x - 15 = 25.

Add 15: 4x = 40.

Divide by 4: x = 10.

2. In standard symbology, x^2 + 3x - 54 = 0. This factors into (x + 9)(x - 6) = 0, so either x + 9 = 0 or x - 6 = 0. Thus either x = -9 or x = 6, and that's the answer.

Answer 6

25 = -3(x+5)+7x = -3x-15+7x = 4x-15
4x = 25+15 = 40
x = 10

x^2+3x-54 = 0
x = [-3+/-sqrt(9+4*54)]/2 = -1.5 +/- 7.5 = (-9, 6)

Answer 7

-3x-15+7x=25
-3x+7x=25+15
4x=40
x=10


Xsquared+3x-54
={x - 6} {x +9}
X=6 or -9