Verified answer

Subtracting x from both sides gives:

4√x = 45 - x.

Then, squaring both sides:

(4√x)^2 = (45 - x)^2

==> 16x = x^2 - 90x + 2025

==> x^2 - 106x + 2025 = 0

==> (x - 81)(x - 25) = 0

==> x = 25 and 81.

Since we squared both sides when we had a radical, we should check for extraneous solutions.

x = 25 ==> LHS: 25 + 4(5) = 45==> LHS = RHS

x = 81 ==> LHS: 81 + 4(9) = 117 ==> LHS ≠ RHS.

Therefore, x = 25 is the only solution.

I hope this helps!

x + 4√x - 45 = 0 ∙ ∙ ∙ ∙ ∙ see it as a quadratic, u² + 4u - 45 = (u - 9)(u + 5), with u = √x

(√x + 9)(√x - 5) = 0

√x = -9

x = ∙ ∙ ∙ ∙ ∙ ∙ no solution

√x = 5

x = 25

your way,

4√x = 45 - x

16x = 2025 - 90x + x²

x² - 106x + 2025 = 0

(x - 25)(x - 81) = 0

x = 25 or x = 81

but squaring both sides MAY introduce an extraneous solution, so we have to check.

25 + 4√25 = 25 + 4(5) = 25 + 20 = 45, solution ∙ ∙ ∙ ∙ ∙ but

81 + 4√81 = 81 + 4(9) = 81 + 36 = 117 <> 45, not a solution

clearly each way works if you're careful.

Yes, but before you do, subtract x from both sides:

4√x = 45 - x

Now square:

16x = 2025 - 90x + x²

Subtract 16x from both sides:

x² - 106x + 2025 = 0

Now use quadratic formula:

x = (106 ± √[106² - 8100])/2

x = (106 ± √3136)/2

x = (106 ± 56)/2

x = 81 or 25.

---Additional notes---

Brian and Philo insist that x=81 is not a solution because 81 + 4√81 = 81 + 4×9 = 117 which does not = 45. They forget that √81 is also -9, and 81 - 4×9 = 45. Therefore, I stand by my answer.

hey u can do 4(x)^1/2=45-x

square both sides now...and solve as a quadratic equation

u will reach on two answers 81 and 25

by substituting in the equation,u can see 25 is the correct answer...

First just leave one side with radical by subtract x from both sides

4sqrt(x) = 45 - x

Now square up both side to get rid of the radical sign

16x = (45 - x)^2

Expand the right side and solve the quadratic equation. You can do it, I know.

Subtract x from both sides, then divide by four so sqrt(x) = (45-x)/4 then square both sides. x = (2025-90x+x^2)/16. So 16x = x^2 -90x+2025. Subtract 16x from both sides. x^2 - 106x +2025 = 0 (x-25)(x-81) = 0. x = 25 or 81. plug them in to get f(25) = 45 f(81) = 117. Thus x = 25.

You might try.

(subtract x from both sides)

4*sqrrt(x) = 45 - x

(now square both sides)

16x = 2025 - 90x + x^2

(now move everything to one side and create a quadratic)

x^2 - 106x + 2025 = 0

(now you can either try factoring or just use the quadratic formula)

(106 +/- sqrrt( (-106)^2 - 4(1)(2025)))/2

x=25, 81

Call:

√x = y

We have:

y^2 + 4y = 45

y^2 + 4y + 4 = 45 + 4

(y + 4)^2 = 49

y + 4 = +/- 7

y = +/- 7 - 4

y = 3 , or y = - 11

a. y = 3

√x = 3

x = 9

b. y = -11,

√x = - 11

no value