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Algebra 2 help

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Q1) Q2) Q3) Q4) Oct 14, 2018

#1
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1.  v^2 -8v  - 59  = -2    add 59 to both sides

v^2  - 8v     =  57       take 1/2 of 8  = 4...square it  = 16....add to both sides

v^2  - 8x + 16  = 57 + 16     factor the left side, simplify the right

(v - 4)^2  =  73      take both roots

x - 4 =  sqrt73          x  - 4  =  -sqrt73

x = 4 + sqr73     or      x =  4 - sqrt73   Oct 14, 2018
#2
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16x^2  + 9y^2

[ 4x  + 3iy ]  [ 4x  - 3iy ]   Oct 14, 2018
#3
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x^2  + 4x  + 13    = 0      subtract 13 from both sides

x^2  +  4x   =  -13         take 1/2 of 4 = 2...square it =  4  add to both sides

x^2  + 4x  +  4 =  -13 + 4        factor the left...simplify the right

(x + 2)^2  = -9     take both roots

x + 2  = sqrt (-9)      or   x + 2  = -sqrt(-9)

x+ 2  = 3i               or     x + 2  = -3i       subtract 2 from both sides

x = -2 + 3i   or    x =  -2 - 3i   Oct 14, 2018
#4
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x^2 + 27  = 0

x^2  = -27       take both roots

x =  sqrt (-27)    or  x   =  -sqrt (-27)

x =   i *sqrt (27)     or    x  =  -i * sqrt (27)

x =  i * sqrt  ( 9 * 3)   or  x   = -i * sqrt (9 * 3)

x = 3isqrt(3)   or x = -3isqrt(3)   Oct 14, 2018