Q: Sqrt 24x 4th divided by sqrt 3x equals?

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Vertical line of symmetry cuts through x = -4 - (sqrt of 3)

Straight to the quadratic equation. -b +/- sqrt(b^2 - 4ac)/2a 16 = a -24 = b 7 = c 24 +/- sqrt[ (-24)^2 - 4(16)(7)]/2(16) 24 +/-sqrt( 576-448)/32 24 +/- sqrt(128)/32 ( reduce fraction ) 3 +/- sqrt(128)/4 ( let us see about that mess under the radical )( like this!) 3 +/- sqrt( 4^2 * 2^2 * 2)/4 (4 and 2 come out and make 8) 3 +/- 8sqrt(2)/4 ( you finish)

12

you can factorise 5x2-24x-12 if you use the quadratic formula: This goes to (24(+/-)sqrt(816))/(10) =5.257 or -0.4566 (4s.f.)

-60

24x. For example, if x is 2, then 24x equals 48.

I'm assuming the question is: 2x2 = 24x x = 0 or x = 12

16xx+24x+9Steps (long):1. Multiply first and third terms:16*9=1442. Factor 144 and find a pair of factors that adds up to the second term (24):144=2*2*2*2*3*32*72, -2*-723*48, -3*-484*36, -4*-366*24, -6*-249*16, -9*-168*18, -8*-1812*12, -12*-123. Rewrite polynomial:16xx+24x+916xx+12x+12x+94. Factor pairs of terms (ie first and second, third and fourth):4x(4x+3)+3(4x+3)5. Combine common terms:(4x+3)(4x+3) --> (4x+3)**2Steps (short):-since twice the product of the square roots of the first and third terms we can place it in the form (ax+c)**2 where a and c are the square roots of the first and third terms respectively16xx+24x+9(ax)**2+b+(c)**22*(sqrt(a**2)*sqrt(c**2))=b2*(sqrt(16)*sqrt(9))=24(sqrt(16)x+sqrt(9))**2(4x+3)**2

x=-.25.

3(2) + 24x + 48 = 0 6 + 24x + 48 = 0 24x + 54 = 0 24x + 54 - 54 = 0 - 54 24x = -54 24x/24 = -54/24 x = -9/4 x = -2 1/4

(x^2) + 24x + 144 = -9 x = -12

√(24x)4/√(3x) = [242x2√(3x)]/3x = 8(24)x√(3x) = 192x√(3x)

x2+24x+144 = 9 x2+24x+144-9 = 0 x2+24x+135 = 0 (x+9)(x+15) = 0 x = -9 or x = -15

24x - 7 = 17

No real roots.

144

x2 + 24x +180 = 0 By using the quadratic equation, you can find that x = -12 + 6i or x = -12 - 6i

The answer is, 24x

If you can't factor it easily, use the quadratic formula.

GCD(15x, 24x) = 3x

24x^5 + 24x^3 = 24x^3(x^2 + 1)

You must add (17n + 144).

5x^2-24x+11

3x2-24x-48 is not factorable.

(24x)^5 - (24x)^3 + (16x)^2 - 16 This can be simplified multiple ways: 1. pull (24x)^3 out of the first two terms and 16 out of the second two. (24x)^3((24x)^2-1) + 16(16x^2-1) 2. just pull 8 out of everything 8(3*(24x)^4-3*(24x)^2+32x^2-2) ...

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