solve for x:        2^x+3=1/8?
492387
This has no solution, 2^x would be equal to a negative number. That can't happen.
843483
using (x+y)^3 = x^3+3x^2y+3xy^2+y^3\n\nwe get (2a+b)^3 = 8a^3+12a^2b+6ab+b^3\n\n(ab+c)^3 = a^3b^3+3a^2b^2c+3abc^2 + c^3\n\n(6ab-c)^3 = 216a^3b^3-108a^2b^2c+18 abc^2 - c^3
572493
=x(x^3-2)\n--> x=0 or x=2^(1/3) or -2^(1/3)
744241
3/(x + 6) - 1/(x - 2) = -8/(x^2 + 4x -12)\n\nStep 1: Create a common denominator for the left side. This is convenient, because (x + 6) * (x - 2)  = (x^2 + 4x - 12)\n3/(x + 6) * (x - 2) / (x - 2) - 1/(x - 2) * (x + 6) / (x + 6)\n3 (x - 2) / ((x + 6) * (x - 2)) - 1 (x + 6) / ((x + 6) * (x - 2))\n\nFinally:\n(3 (x - 2) - 1 (x + 6)) / (x^2 + 4x -12) = -8/(x^2 + 4x -12)\n\nStep 2: Cancel the x^2 + 4x -12 denominator on both sides, then solve.\n(3 (x - 2) - 1 (x + 6)) / (x^2 + 4x -12) = -8/(x^2 + 4x -12)\n3 (x - 2) - 1 (x + 6) = -8\n3x - 6 - x - 6 + 8 = 0\n2x - 4 = 0\n2x = 4\nx = 2 (solution!)
685308
(3x + 6/4(x^2)) (x + 2/16(x))\ntake out x\n=x(3 + 3/2(x)).x(1 + 1/8)\n=9/8(x^2)(3 + 3/2(x))\ncan simplify d numbers still.
901403
Do you mean\n\n3^(x+5) = 9^x → 3^(x+5) = 3^(2x)  → x = 5\n\nOr\n\n3^x+5 = 9^x\nie 3^(2x) = 3^x + 5\nSo [3^(x)]² - 3^x - 5 = 0\nLet v = 3^x\nThus v² - v - 5 = 0\nSo v = ½{1 ± √[(-1)² - 4.(1)*(-5)]}\n= ½ (1 ± √21)\nSince v = 3^x and we seek real solutions\nv = ½ (1 + √21)\nSo 3^x = ½ (1 + √21)\nx = log [½ (1 + √21)] / log3\n≈ 0.9344\n\nCheck\nLHS = 3^x + 5 ≈ 3^(0.9344) + 5 ≈ 7.791\nRHS = 9^x ≈ 9^(0.9344) ≈ 7.792 (Differences are from truncation errors)
747340
-2x-x > -6 + 4\n-3x > -2 \nx < 2/3
83153
There are a couple of ways to work this out, I will take the easiest to explain.\n\n(x-3)(x^3+3x^2+9x+27) Can be rewritten as:\n\n(x)(x^3+3x^2+9x+27)+(-3)(x^3+3x^2+9x+27) Now, multiply those out.\n\nx^4+3x^3+9x^2+27x-3x^3-9x^2-27x-81 Now, sort by like powers of x\n\nx^4+3x^3-3x^3+9x^2-9x^2+27x-27x-81 Simplify\n\nx^4-81
943154
3= 1/2x+3\n\n>>>>1/2x=0,>>>x=0\n\ni hope that this helps
774014
2^3+2*2^2-3(2)-10=8+8- 6 -10 =0\nTherefore x-2 is a factor of the given polynomial
706334
To solve #1, you  have to use partial fractions.  \n\nYou have to convert \n\n** x / [(3x-1)(x+2)] = A/(3x-1) + B/(x+2) for some constants A,B.\n\nTaking the integral of x / [(3x-1)(x+2)] would be the same as taking the integral of A/(3x-1) + B/(x+2), so let's do that.\n\nIntegral (A/(3x-1) + B/(x+2))dx = \nIntegral (A/(3x-1))dx + Integral (B/(x+2))dx\n\nAlways pull out constants.\n\nA*Integral(1/(3x-1))dx + B*Integral(1/(x+2))dx\nA * 1/3 * ln |3x - 1| + B * ln|x+2| + C\n\nNow, solve for A and B using the equation marked as **.\n\nx / [(3x-1)(x+2)] = A/(3x-1) + B/(x+2)\n\nFirst, multiply both sides by (3x-1)(x+2) to get\n\nx = A(x+2) + B(3x -1)\n\nRemember that the above is a statement that is __true for all x___, so in order to solve for A and B, we can let x be ANY value.\n\nFor simplicity purposes, we're going to let x=-2 and then x=1/3.\n\nx = -2:  \n\n-2 = A(-2 + 2) + B(3(-2) - 1)\n-2 = B(-7)\nB = 2/7\n\nx = 1/3:\n\n1/3 = A(1/3 + 2) + B(3(1/3) -1)\n1/3 = A(7/3)\nA = 1/7\n\nTherefore, substitute A=1/7 and B=2/7 back into here:\n\nA * 1/3 * ln |3x - 1| + B * ln|x+2| + C\n\nto get\n\n1/7 * 1/3 * ln |3x - 1| + 2/7 * ln|x+2| + C\n7/3 * ln |3x - 1| + 2/7 * ln|x+2| + C\n\nTo solve #2:\n\nUse integration by parts.\n\nlet u = arcsin(3x)                  dv = dx\ndu = 1/sqrt(1-(3x)^2) * 3         v = x\n\nSo our new integral becomes\n\nx*arcsin(3x) - Integral [ (3x)/sqrt(1 - (3x)^2) ] dx\n\nAfter that it becomes substitution.
453667
y=(x+8)^3-5\ny+5=(x+8)^3\n(y+5)^(1/3)=x+8\nx=(y+5)^(1/3)-8
961234
Let x = y^(1/3)\nx^2 - 9x + 8 = 0\n(x - 8)(x - 1) = 0\nx = 8 or 1\ny^(1/3) = 8 or 1\ny = 2 or 1
920343
(4/3)[x^3/(2-x)]^(1/3)\n[(2-x)(3)x^2-x^3(-1)]/\n(2-x)^2=\n\n 4x[1/(2-x)]^(1/3)\n[3x^2(2-x)+x^3]/\n3(2-x)^2
267923
3^x=2^x/2\n\n(1.5)^x=0.5\n\nx=-1.71
541499
2x(x-5)-3(2x+1)\n2x^2-10x-6x-3\n2x^2-16x-3
135330
First you need to take the anti-derivative (integral) of the equation.\n\nSo, 1/3 (3x^3) - 2x + C = y (you always need to put in that constant when you integrate).\n\nSo, x^3 - 2x + C = 2 when x= -1... (-1)^3 - (-2) + C= 2...  \nSo, -1 + 2 + C= 2... 1 + C = 2... C=1...\n\nFinal answer: y= x^3 -2x +1