I try to do this problem just cant seem to get it. SQRT58+9x = x + 4 What is X?

　
I assume you REALLY mean: SQRT(58+9x)
Please don't be stingy with parentheses.
They are required here.

√(58+9x) = x+4

Square both sides

58 + 9x = x² + 8x + 16
x² − x − 42 = 0
(x + 6) (x − 7) = 0
x = −6, x = 7

Check for extraneous solutions that might have been introduced by squaring.

x = −6
√(58+9x) = √(58−54) = √4 = 2
x + 4 = −6+4 = −2
NOT a solution

x = 7
√(58+9x) = √(58+63) = √121 = 11
x + 4 = 7+4 = 11
OK

Solution: x = 7

√(58 + 9x) = x + 4
[√(58 + 9x)]² = (x + 4)²
58 + 9x = x² + 8x + 16
x² - x - 42 = 0
(x + 6)(x - 7) = 0
x + 6 = 0 or x - 7 = 0
x = -6 or x = 7

Check :
When x = -6 :
L.H.S. = √[58 + 9(-6)] = 2
R.H.S. = (-6) + 4 = -2
Since L.H.S. ≠ R.H.S., x = -6 is rejected.

When x = 7 :
L.H.S. = √[58 + 9(7)] = 11
R.H.S. = (7) + 4 = 11
Since L.H.S. = R.H.S., x = 7 is a root of the equation.

Answer: x = 7

sqrt(58) + 9x = x + 4
sqrt(58) = -8x + 4
Squaring
58 = ( -8x + 4)^2
58 = 64x^2 -64x + 16
64x^2 - 64x -42 = 0
x^2 - x -42/64 = 0
x^2 - x - 21/32 = 0
Complete the Square
x^2 - x = 21/32
(x - 1/2)^2 - (1/2)^2 = 21/32
(x - 1/2)^2 = 21/32 + 8/32 (NB 8/32 = 1/4)
(x - 1/2)^2 = 29/32
Square Rooting
x - 1/2 = +/-sqrt(9) / 4sqrt(2) = 4sqrt(9/2)
x = 1/2 +/- 4sqrt(9/2)
x = 1/2 +/- 4sqrt(4.5)

sqrt(58) + 9x = x + 4

Subtract 9x from both sides

sqrt(58) = -8x + 4

Square both sides

58 = (-8x + 4)^2

FOIL the right side

58 = 64x^2 - 64x + 16

Subtract 58 from both sides

64x^2 - 64x - 42 = 0

Divide both sides by 2

32x^2 - 32x - 21 = 0

Put in quadratic formula to get

x = 1/2 ± sqrt(29/2)/4

However, only the negative form works when you plug it in.

This is a really annoying answer, so maybe you meant to put the parenthesis around what was being square-rooted?




sqrt(58 + 9x) = x + 4

Square both sides

58 + 9x = (x+4)^2

FOIL the right side

58 + 9x = x^2 + 8x + 16

Subtract 9x and 58 from both sides

0 = x^2 - x - 42

Factor the right side

0 = (x + 6)(x - 7)

Plug in each term being multiplied for 0

x = -6, 7

Plug in both of these into your original equation and only 7 works

x = 7

I hope this helped! Please pick a best answer. Whether the best answer you choose is or isn't mine is your choice! :)

Is the sqrt is of the whole 58+9x ?
And if it is, it's very simple. You just have to square both the sides then the root will be gone. Like this:
58+9x=(x+4)²
And I think you can solve it now?

square both sides
58+9x = x^2+8x+16
0 = x^2 -x -42
0 = (x + 6) (x - 7)
Therefore x= -6 or x=7