Simplify Radicals
Simplify.
2 sqrt(72)
2 sqrt(2*2*2*3*3)
2*2*3 sqrt(2)
12 sqrt(2)
Factor:
7x^2 + 14x
7x(x+2)
Factor Completely:
x^3+4x^2+8x+32
4 terms, group to factor
(x^3+4x^2)+(8x+32)
x^2(x+4)+8(x+4)
(x+4)(x^2+8)
Solve.
x^2-4=12
No x term, so use the square root method
x^2=16
sqrt(x^2)=sqrt(16)
x=+-4
Solve.
(x + 5)(2x - 6) = 0
Already factored so set each factor =0 to solve
x+5=0 and 2x-6=0
x=-5 and x=3
Simplify.
root 3 (128)
root 3 (2*2*2*2*2*2*2)
2*2root 3 (2)
4 root 3 (2)
Factor Completely:
x^2-8x+12
Multiplies to 12:
-6 * -2
Adds to -8:
-6 + -2
(x-6)(x-2)
24a^2b^3+12a^3b
Factor:
12a^2b(2b^2+a)
Solve.
7x^2 + 84 = -49x
Add 49x to bring to left side of equation
7x^2+49x + 84 =0
7(x^2+7x + 12) =0
Multiplies to 12:
4*3
Adds to 7:
4+3
7(x+4)(x+3) =0
take each factor set =0 to solve
x+4=0 and x+3=0
x=-4 and x=-3
Solve.
x^2+9x+20=0
Multiplies to 20:
4*5
Adds to 9:
4+5
(x+4)(x+5) =0
take each factor set =0 to solve
x+4=0 and x+5=0
x=-4 and x=-5
Simplify.
2/(sqrt(80))
2/(sqrt(80))
2/(4 sqrt(5))
1/(2 sqrt(5))
(1 sqrt(5))/(2 sqrt(5)sqrt(5))
sqrt(5)/(2*5)
sqrt(5)/10
Factor Completely:
25x^2-36
Both perfect squares and subtraction. Difference of Squares
(5x)^2-(6)^2
(5x+6)(5x-6)
Factor Completely:
-3y^2+6y+72
-3(y^2-2y-36)
Multiplies to -36:
4*-6
Adds to -2:
4+ -6
3(y-6)(y+4)
Solve.
3x^2 + 7x = 40
Subtract 40x to bring to left side of equation
3x^2 + 7x-40=0
Multiplies to 3*-40 which is -120:
-8*15
Adds to 7:
-8+15
3x^2 -8x+15x-40=0
[x(3x-8)+5(3x-8)]=0
(3x-8)(x+5)=0
take each factor set =0 to solve
3x-8=0 and x+5=0
x=8/3 and x=-5
Solve.
3x^2-8=13
No x term, so use the square root method
3x^2=21
x^2=7
sqrt(x^2)=sqrt(7)
x=+-sqrt7
Simplify.
root 3 (1750)
root 3 (2*5*5*5*7 )
5root 3 (2*7)
5root 3 (14)
Factor Completely:
x^2+4
Prime
This is not a difference of squares, its the SUM and no GCF so it cannot be factored.
Factor completely:
x^3+3x^2-4x-12
4 terms, group to factor
(x^3+3x^2)+(-4x-12)
[x^2(x+3)-4(x+3)]
(x+3)(x^2-4)
now we see the difference of squares
(x+3)[(x)^2-(2)^2]
(x+3)(x+2)(x-2)
Solve.
(x+4)^2=49
No x by itself term, so use square root method
sqrt((x+4)^2)=sqrt(49)
x+4 =+-7
x=+-7-4
Two answers
x=7-4 and x=-7-4
x=3 and x=-11
Solve.
3x^2-2x=2x+7
Subtract 2x and subtract 7 to bring to left side of equation
3x^2-2x-2x-7=0
3x^2-4x-7=0
Multiplies to 3*-7 which is -21:
3*-7
Adds to -4:
3+ -7
3x^2+3x-7x-7=0
3x(x+1)-7(x+1)=0
(x+1)(3x-7)=0
take each factor set =0 to solve
x+1=0 and 3x-7=0
x=-1 and x=7/3
Simplify.
root 3 (3/16)
root 3 (3)/root 3 (16)
root 3 (3)/root 3 (4*4)
(root 3 (3)root 3 (4))/(root 3 (4*4)root 3 (4))
root 3 (12)/4
Factor Completely:
6x^2-34x-40
2(3x^2-17x-20)
Multiplies to 3*-20 which is -60:
3*-20
Adds to -17:
3+ -20
2(3x^2+3x-20x-20)
2[3x(x+1)-20(x+1)]
2(x+1)(3x-20)
Factor Completely:
9x^2-42x+49
Front and back are perfect squares
(3x)^2-2(3x)(7)+(7)^2
Middle is =-42x, so its a perfect square trinomial:
(3x-7)^2
Solve.
6x^2+9x-6=0
6x^2+9x-6=0
3(2x^2+3x-2)=0
Multiplies to 2*-2 which is -4:
-1*4
Adds to 3:
-1+4
3(2x^2-1x+4x-2)=0
3[x(2x-1)+2(2x-1)]=0
3(2x-1)(x+2)=0
take each factor set =0 to solve
2x-1=0 and x+2=0
x=1/2 and x=-2
Solve.
2(x-3)^2+6=56
No x by itself term, so use square root method
2(x-3)^2=50
(x-3)^2=25
sqrt((x-3)^2)=sqrt(25)
x-3=+-5
x=+-5+3
Two answers
5+3 and -5+3
x=8 and x=-2