Term
Factor the expression
x2-6x+5 |
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Definition
x2-6x+5 =(x-1)(x-5)
because
(-1)+(-5)=-6
(-1)(-5)=5 |
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Term
Solve the equation by factoring
x2-9x+14=0 |
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Definition
1. factor it:
x2-9x+14=0
(x-2)(x-7)=0
2. use zero product property
x-2=0 or x-7=0
x=2 or x=7 |
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Term
Factor the expression
x2+x-12 |
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Definition
To factor the expression find two numbers m and n, where
m+n=1, mn=-12
x2+x-12=(x-3)(x+4) |
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Term
Factor the expression
x2+21x+98 |
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Definition
To factor the expression find two numbers m and n, where
m+n=21, mn=98
x2+21x+98=(x+7)(x+14) |
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Term
Factor the expression
x2-2x-35 |
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Definition
To factor the expression find two numbers m and n, where
m+n=-2, mn=-35
x2 -2x-35=(x-7)(x+5) |
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Term
Factor the expression
x2+6x+9 |
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Definition
To factor the expression find two numbers m and n, where
m+n=6, mn=9
x2+6x+9=(x+3)(x+3)=(x+3)2 |
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Term
Factor the expression
2x2-14x+12 |
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Definition
To factor the expression find two numbers m and n, where
m+n=-14, mn=2*12=24
2x2-14x+12=2(x+(-2)/2)(x+(-12)/2)=2(x-1)(x-6)
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Term
Factor the expression
3x2+10x-8 |
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Definition
To factor the expression find two numbers m and n, where
m+n=10, mn=3·(-8)=-24
3x2+10x-8=3(x+12/3)(x+(-2)/3)=
3(x+4)(x-2/3)=(x+4)(3x-2) |
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Term
Factor the expression
42x2+35x+7 |
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Definition
To factor the expression factor out GCF 7(6x2+5x+1) and find two numbers m and n, where
m+n=5, mn=6•1=6
7•6(x+2/6)(x+3/6)=
=42(x+1/3)(x+1/2) |
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Term
Factor the expression
-15x2+3x+12 |
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Definition
To factor the expression factor out GCF -3(5x2-x-4) and find two numbers m and n, where
m+n=-1, mn=5•(-4)=-20
-3•5(x+(-5)/5)(x+4/5)=
=-15(x-1)(x+4/5) |
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Term
Solve the equation by factoring
x2+4x=21 |
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Definition
1. move 21 to the right and factor it:
x2+4x-21=0
(x+7)(x-3)=0
2. use zero product property
x+7=0 or x-3=0
x=-7 or x=3 |
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Term
Solve the equation by factoring
x2=13x-42 |
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Definition
1. move 13x-42 to the right and factor it: x2-13x+42=0
(x-6)(x-7)=0
2. use zero product property
x-7=0 or x-6=0
x=7 or x=6 |
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Term
Solve the equation by factoring
9x-8=x2 |
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Definition
1. move 9x-8 to the left and factor it: x2-9x+8=0
(x-1)(x-8)=0
2. use zero product property
x-1=0 or x-8=0
x=1 or x=8 |
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Term
Solve the equation by factoring
2x2+x=x2+20 |
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Definition
1. move x2+20 to the right, simplify and factor it: x2+x-20=0
(x-4)(x+5)=0
2. use zero product property
x-4=0 or x+5=0
x=4 or x=-5 |
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Term
Solve the equation by factoring
3x2-8x-19=(x-1)2 |
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Definition
1. 3x2-8x-19=x2-2x+1
Move x2-2x+1 to the left and simplify 2x2-6x-20=0, factor out GCF
2(x2-3x-10)=0, factor completely
2(x-5)(x+2)=0
2. use zero product property
x+2=0 or x-5=0
x=-2 or x=5 |
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Term
Solve the equation by finding square root
x2=289 |
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Definition
x2=289
x=√289=17
or
x=-√289=-17 |
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Term
Solve the equation by finding square root
x2+169=0 |
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Definition
x2+169=0
x2=-169
x=√-169=√(-1)•√169=13i
or
x=-√-169=-√(-1)•√169=-13i |
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Term
Solve the equation by finding square root
1/2 x2-8=16 |
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Definition
1/2 x2-8=16
move -8 to the right
1/2x2=16+8=24
multiply by 2 both sides of your equation
x2=48
take square root of both sides of your equation
x=√48=√16•3=4√3
or
x=-√48=-√16•3=-4√3
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Term
Solve the equation by finding square root
(3x+2)2-49=0 |
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Definition
(3x+2)2-49=0
(3x+2)2 =49
take square root of both sides of your equation
3x+2=7 or 3x+2=-7
3x=5 or 3x=-9
x=5/3 or x=-9/3=-3 |
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Term
Solve the equation
x2-19=0 |
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Definition
x2-19=0
x2 =19
x=√19 or
x=-√19 |
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Term
Solve the equation using the quadratic formula
x2+4x-2=0 |
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Definition
x2+4x-2=0
a=1 b=4 c=-2
D=b2-4ac=(4)2-4•1•(-2)=16+8=24
D>0, equation has two real roots
x1=(-b+√D)/2a=(-4+√24)/2=
=(-4+√4•6)/2=
=(-4+2√6)/2=(factor out 2)=
=2(-2+√6)/2=-2+√6
x2=(-b-√D)/2a=(-4-√24)/2=
=(-4-√4•6)/2=
=(-4-2√6)/2=(factor out 2)=
=2(-2-√6)/2=-2-√6
Answer:
x1=-2+√6
x2=-2-√6 |
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