Solve for x exactly without using a calculator or table: 7^(x+2)=49^(x+6)?
347583
49 can be written as 7^2\nThus,\n49^(x+6) = 7^[2(x+6)]\nThis is equal to 7^(x+2)\nIf the bases are the same, then the exponents must be the same.  That is\n2(x+6) = x+2\n2x+12 = x+2  Subtract x from each side\nx+12 = 2  Subtract 12 from each side\nx = -10
741586
set y=0\nsolve quadratic eqn\nquadratic eqn\n\n-7 +- (49-16)^.5\n-------------------\n2\n= (-7 +- 33^.5)/2
258077
X = -1\nf(-1) = 4*(1/7) = 4/7\n\nX = 1\nf(1) = 4*7 = 28\n\nX = 2\nf(2) = 4*7^2 = 4*49 = 196
333624
(ln x)^7=(7*(lnx)^6)*(1/x)=7*(lnx)^6/x
61186
This answer can be easily explained using algebra. Let x=your number. Then step by step here is your expression:\n\nx\n2x\n2x+5\n2x+5+12=2x+17\n2x+17-3=2x+14\n(2x+14)/2=x+7\nx+7-x=7\nSo the answer is always 7, no matter what x is.
812111
x^2 = 96\n\nx= +/- sqrt(96) = +/- 4 sqrt(6)
363348
Are we solving for x?
288394
well lets take the first example- ok so the middle number is 11. and the number with no 'x' in it is 30. what makes 30 = 6 x 5 or 3 x 10. so try adding and subtracting those numbers in your mind: 6+5=11 ... 3+10=13 ...6-5=1...5-6=-1...10-3=7...3-10=-7. so which one of those give 11  ->> 6 + 5. \nso all u do is x^2+ 6x + 5x + 30 [split 11 as 6 + 5]\nur next step ; take 'x' common for the first to terms and 5 common for the 2nd two terms, u get\nx(x+6)+ 5(x+6)\ntake the bracket term multiplied by the un-bracket terms\n(x+5)(x+6)\n\nvoila...problem solved
738884
x^2-5x-14=0\n=>x^2-7x+2x-14=0\n=>x(x-7)+2(x-7)=0\n=>(x-7)(x+2)=0\nTherefore either x-7=0 or x+2=0\nIf x-7=0,then x=7,and if x+2=0,then x=_2\nThereforex=7 or -2 ans
735202
You mean find solutions for x when 2x^2+12x+18=0.\n\n  First we can divide thru by 2 just to make it simpler.\n x^2+6x+9=0 , then factor and get\n(x+3)^2=0\nso x=3.
982146
Just add and substract terms in both sides.\n\nSince \ny-x^2+8x\nis equal to 7, \nyou can add x^2 and substract 8x to both sides.\n(y-x^2+8x) +x^2-8x = y\n7 +x^2-8x = x^2-8x+7\n\nso y=x^2-8x+7\n\nby the way, if you factorize in terms of x then you'd get\ny=(x-1)(x-7)
544837
I squared the 7 to start with and got 49.  I am also only showing the addition version, you can do the subtraction later yourself.\n\n(-7 + sqrt(49 - 4(9)(-1)))/2(9)\n(-7 + sqrt(49 - -36))/18\n(-7 + sqrt(49 + 36))/18\n(-7 + sqrt(85))/18\n\nand I think that that is it.  You cannot simplify the square root.
741076
1/x+3/x+2=7\nMultiply by x getting:\n1+3+2x =7x\n4-5x =0\n0x* -5x +4 =0\n\n7/2x+2/x-1=4\nMultiply by 2x getting:\n7 +4 -2x =8x\n11-10x = 0\n0x* -10x +11 = 0\n\nx*+7x+2=2x+4\nx* +7x -2x +2 -4=0\nx* +5x -2 = 0\n\n4x*-3x=2x*+7 \n4x* -2x*-3x -7 =0\n2x*-3x-7 =0\n\n2x+3/x-1=x/4\nMultiply by x getting:\n2x* +3 -2x = x*/4\n2x* - x*/4 -2x +2=0\n2.25x* -2x +2 = 0\n\nThere, its done simply by multiplying and transposing terms to get what you want. You can move any term from one side of the equation to the other as long as you change its sign fro minus to plus or plus to minus.
891369
x^2 + 5x - 14 = 0\nx^2 -2x + 7x -14 = 0\nx(x -2) + 7(x-2) = 0\n(x + 7)(x - 2) = 0\nEither x+7 or x-2 = 0\nPut x + 7 = 0\nx= -7\nPut x-2 = 0\nx = 2\nThere are two roots\nx = 2,-7
530142
use the quadratic equation:\nx=-b +/- the square root of b^2 - 4ac all over 2a\na=1,b=7,c=10 so plug it in\nx=-7 +/- the square root of 49-40 all over 2\n-7 +3 = -4 divided by 2 x=-2\n-7-3=-10 divided by 2 = -5\nso x = -2 or x=-5
858168
1. 14x^2 +21x\n\na good way to start would be to factor out any common terms:\n\n7(2x^2 + 3x)\n\n7x(2x + 3)
1126492
Use pythagorean theorem.\n\n3^2 + 7^2 = hypotenuse (diagonal) squared\n\n9 + 49 = x^2\n\n58 = x^2\n\nsquare root of both sides  diagonal is = 7.61577  feet\n\n(or 7 feet 7.4 inches)