Advanced Algebra

Quadratic Functions

100

x²-11x+30=0

x=[5,6]

200

3x²+7x-6=0

x=[2/3,-3]

300

5x²+5x-5=0

x=(-1+-√5)/2

400

2x²-8x-24=0

x=[6,-2]

500

9x²-3/x=-6

x=[1/3,-1]

Systems of Equations

100

2x+5y=19

y=3x-3

x=2

y=3

200

y=3x-1

4x+y=-8

x=-1

y=-4

300

3x-y=7

x+2y=21

x=5

y=8

400

x+y-z=0

2x-3y+z=1

2x+y+2z=7

x=1

y=1

z=2

500

x-3y+3z=-4

2x+3y-z=15

4x-3y-z=19

x=5

y=1

z=-2

Exponential & logarithmic functions

100

log 4ⁿ=5/2

32

200

4^x+1=32

x=3/2

300

log₄(2x²-4x)=2

x=[4,-2]

400

4ln(7x+4)+1=13

x=(e³-4)/7

500

log₆x+log₆(x+5)=2

x=4

Polynomial Function

100

(x-5)(x+5)

x=[5,-5]

200

2(x^2+4x+4)=0

x=-2

300

Expand (4x+7)(x²-x-1)

4x³+3x²-11x-7

400

Expand (6x²-3)(6x²+3)

36x⁴-9

500

(x²-6x+3)(x²-2x+2)

x⁴-8x+17x²-18x+6

Radical Functions

100

³√x¹⁵

x⁵

200

³√(x)-6=-2

x=64

300

√(8x+60)=x+5

x=5

400

⁴√(81x²y¹⁸)

3x^1/2y^9/2

500

√(3x²+10x)-5=0

x=[5/3,-5]