Basic Math Examples

Solve for m m^3=8
m3=8m3=8
Step 1
Subtract 88 from both sides of the equation.
m3-8=0m38=0
Step 2
Factor the left side of the equation.
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Step 2.1
Rewrite 88 as 2323.
m3-23=0m323=0
Step 2.2
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2)a3b3=(ab)(a2+ab+b2) where a=ma=m and b=2b=2.
(m-2)(m2+m2+22)=0(m2)(m2+m2+22)=0
Step 2.3
Simplify.
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Step 2.3.1
Move 22 to the left of mm.
(m-2)(m2+2m+22)=0(m2)(m2+2m+22)=0
Step 2.3.2
Raise 22 to the power of 22.
(m-2)(m2+2m+4)=0(m2)(m2+2m+4)=0
(m-2)(m2+2m+4)=0(m2)(m2+2m+4)=0
(m-2)(m2+2m+4)=0(m2)(m2+2m+4)=0
Step 3
If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.
m-2=0m2=0
m2+2m+4=0m2+2m+4=0
Step 4
Set m-2m2 equal to 00 and solve for mm.
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Step 4.1
Set m-2m2 equal to 00.
m-2=0m2=0
Step 4.2
Add 22 to both sides of the equation.
m=2m=2
m=2m=2
Step 5
Set m2+2m+4m2+2m+4 equal to 00 and solve for mm.
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Step 5.1
Set m2+2m+4m2+2m+4 equal to 00.
m2+2m+4=0m2+2m+4=0
Step 5.2
Solve m2+2m+4=0m2+2m+4=0 for mm.
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Step 5.2.1
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2ab±b24(ac)2a
Step 5.2.2
Substitute the values a=1a=1, b=2b=2, and c=4c=4 into the quadratic formula and solve for mm.
-2±22-4(14)212±224(14)21
Step 5.2.3
Simplify.
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Step 5.2.3.1
Simplify the numerator.
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Step 5.2.3.1.1
Raise 22 to the power of 22.
m=-2±4-41421m=2±441421
Step 5.2.3.1.2
Multiply -414414.
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Step 5.2.3.1.2.1
Multiply -44 by 11.
m=-2±4-4421m=2±44421
Step 5.2.3.1.2.2
Multiply -44 by 44.
m=-2±4-1621m=2±41621
m=-2±4-1621m=2±41621
Step 5.2.3.1.3
Subtract 1616 from 44.
m=-2±-1221m=2±1221
Step 5.2.3.1.4
Rewrite -1212 as -1(12)1(12).
m=-2±-11221m=2±11221
Step 5.2.3.1.5
Rewrite -1(12)1(12) as -112112.
m=-2±-11221m=2±11221
Step 5.2.3.1.6
Rewrite -11 as ii.
m=-2±i1221m=2±i1221
Step 5.2.3.1.7
Rewrite 1212 as 223223.
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Step 5.2.3.1.7.1
Factor 44 out of 1212.
m=-2±i4(3)21m=2±i4(3)21
Step 5.2.3.1.7.2
Rewrite 4 as 22.
m=-2±i22321
m=-2±i22321
Step 5.2.3.1.8
Pull terms out from under the radical.
m=-2±i(23)21
Step 5.2.3.1.9
Move 2 to the left of i.
m=-2±2i321
m=-2±2i321
Step 5.2.3.2
Multiply 2 by 1.
m=-2±2i32
Step 5.2.3.3
Simplify -2±2i32.
m=-1±i3
m=-1±i3
Step 5.2.4
The final answer is the combination of both solutions.
m=-1+i3,-1-i3
m=-1+i3,-1-i3
m=-1+i3,-1-i3
Step 6
The final solution is all the values that make (m-2)(m2+2m+4)=0 true.
m=2,-1+i3,-1-i3
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