Show EACH step involved in solving the following equation.?

Question

Be sure to check your solutions (tell if any of them are extraneous):
sqrt(3x + 4) + x = 8
This what I have so far, but I'm stuck.
sqrt(3x +4) + x = 8
sqrt(3x + 4)^2 = (x+8)^2
3x+4 = x^2 -16x + 64

-60 = x^2 -19x
Where do I go from here or am I way off track?

Answer 1

When you take x from both sides the right hand side should be (x-8)^2 but you somehow have corrected this by the time you get to the last line.

You need to solve the quadratic you have

(x-15)(x-4)=0

so x is either 15 or 4.

However as we have had to square the equation we may have introduced wrong answers so try plugging in the potential solutions

if x = 15 then sqrt(3x+4)+x= 22 so x=15 actually isn't a solution at all.

if x= 4 then sqrt(3x+4)+x=8 as required.

So the only solution is x=4

Answer 2

sqrt(3x +4) + x = 8
sqrt(3x +4) = 8 -x (Subtraction)
(sqrt(3x + 4))^2 = (-x + 8) ^2 (Square both sides)
3x+4 = x^2 -16x + 64
0 = x^2 -19x + 60 (Subtraction)
0 = x^2 - 4x - 15x + 60 (Factor By Grouping)
0 = (x^2 -4x) - (15x +60)
0 = x(x -4) - 15(x -4)
0 = (x-15)(x-4)
(x-15) = 0 | (x -4) = 0 (Each Term Equal to Zero)
x = 15 | x = 4
Check:

sqrt(3(15) + 4) + 15 = 8
sqrt(49) + 15 = 8
7 + 15 = 8
22 != 8
15 is not a solution

Check:

sqrt(3(4) + 4) + 4 = 8
sqrt(16) + 4 = 8
4 + 4 = 8
8 = 8
4 is the solution

Answer 3

You made a small mistake at the start ... you SUBTRACT x from bothe sides of the equation first

sqrt (3x+4) + x = 8
srqt (3x + 4 ) = 8 - x
(sqrt (3x + 4 ))^^2 = (8 -x) ^^ 2
3x + 4 = 64 - 16x + x^^2
0 = x^^2 -16x + 64 - 3x - 4
0 = x^^2 - 19x + 60
0 = ( x - 15)(x - 4)

x = 15 or x = 4

Check

Try x = 15
sqrt(49) + 15 = +/-7 +15 = 8 (true if we take the -7 root of 49)

Try x = 4

sqrt(16) + 4 = +/-4 + 4 = 8 (true if we take the +4 root of 16)

Remember for positive numbers, their square root is may be either positive of negative.

Answer 4

sqrt(3x + 4) + x = 8

Bring the x over to the right hand side, to get

sqrt(3x + 4) = 8 - x

Now, square both sides, to get rid of the square root symbol.

3x + 4 = (64 - 16x + x^2)

Bring everything over to the right hand side, to get

0 = 60 - 19x + x^2

Let's rearrange that into the way we're used to seeing quadratics.

x^2 - 19x + 60 = 0

{Note; you were off track in the sense that whenever we have a mixtures of x^2 terms and x terms, we need to bring everything to one side and equate it to 0, where we can factor}.

Now, we factor

(x - 15) (x - 4) = 0

This gives us the solutions x = {4, 15}
We can't assume both will work though, so we must plug each into the original equation to see if we get the right answer.

let x = 4: sqrt(3(4) + 4) + 4 = sqrt (16) + 4 = 4 + 4 = 8, so this works.

Let x = 15: sqrt (3(15) + 4) + 15 = sqrt (49) + 15 = 22, which doesn't work, so we reject this solution.

Our final answer is x = 4

Answer 5

Your equation can be arranged further as:
0 = x^2 - 19x + 60.
You can use the quadratic formula, or, if you're slick, just simply see that you can factor:
0 = (x - 15)(x - 4).
Double-check by multiplying those binomials...

So the equation will hold if either (x - 15) is zero or (x - 4) is zero.

So your solution set would be {4, 15}; however, if you check the solutions again with the original equation, you'll find:

sqrt(3*[4] + 4) + [4] = 8, indeed.
but
sqrt(3*[15] + 4) + [15] = 8, not so

So your answer is 4.

Answer 6

√3x + 4 + x = 8

√3x + 4 + x - x = 8 - x

√3x + 4 = 8 - x

√3x + 4 = (- x + 8)²

3x + 4 = x² - 16x + 64

3x + 4 - 3x = x² - 16x + 64 - 3x

4 = x² - 19x + 64

4 - 4 = x² - 19x + 64 - 4

0 = x² - 19x + 60

0 = (x - 15)(x - 4)

- - - - - - - - - - - -

Roots

x - 15 = 0

x - 15 + 15 = 0 + 15

x = 15

- - - - - - - -

x - 4 = 0

x - 4 + 4 + 0 + 4

x = 4

- - - - - - - s-

Answer 7

5/6 x + 3 = a million/2 x subtract a million/2 x from the two factors 2/6 x + 3 = 0 replace 2/6 x right into a million/3 x (simplifying a fraction) which will properly be written as x/3 x/3 + 3 = 0 subtract 3 from the two factors x/3 = -3 multiply the two factors via 3 x = -9

Answer 8

sq rt of {(3x + 4) + x}

let x equal variable numbers until you find the right one.

Let x = 15

3 x 15 + 4 + 15

45 + 4 + 15

= 64

root of 64 = 8

Answer 9

a bit off the track cuz
sqrt(3x+4) +x=8
3x+4=(8-x)^2 !!!!!!!!!
3x+4=64-16x+x^2
x^2 -19x +60=0
x^2 -15x -4x +60=0
x(x-15)-4(x-15)=0
x=15 or x=4

Answer 10

sqrt(3x +4) + x = 8
(3x + 4) = (8-x)^2
3x+4 = x^2 -16x + 64
x^2 -16x + 64-3x-4=0
x^2 -19x + 60=0

x1=1/2*[19+root(19*19-4*60)]
x1=1/2*[19-root(19*19-4*60)]

simplify by yourself