Finite Math Examples

Find the Roots (Zeros) f(x)=3(x-8)^2-27
f(x)=3(x-8)2-27f(x)=3(x8)227
Step 1
Set 3(x-8)2-27 equal to 0.
3(x-8)2-27=0
Step 2
Solve for x.
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Step 2.1
Simplify 3(x-8)2-27.
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Step 2.1.1
Simplify each term.
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Step 2.1.1.1
Rewrite (x-8)2 as (x-8)(x-8).
3((x-8)(x-8))-27=0
Step 2.1.1.2
Expand (x-8)(x-8) using the FOIL Method.
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Step 2.1.1.2.1
Apply the distributive property.
3(x(x-8)-8(x-8))-27=0
Step 2.1.1.2.2
Apply the distributive property.
3(xx+x-8-8(x-8))-27=0
Step 2.1.1.2.3
Apply the distributive property.
3(xx+x-8-8x-8-8)-27=0
3(xx+x-8-8x-8-8)-27=0
Step 2.1.1.3
Simplify and combine like terms.
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Step 2.1.1.3.1
Simplify each term.
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Step 2.1.1.3.1.1
Multiply x by x.
3(x2+x-8-8x-8-8)-27=0
Step 2.1.1.3.1.2
Move -8 to the left of x.
3(x2-8x-8x-8-8)-27=0
Step 2.1.1.3.1.3
Multiply -8 by -8.
3(x2-8x-8x+64)-27=0
3(x2-8x-8x+64)-27=0
Step 2.1.1.3.2
Subtract 8x from -8x.
3(x2-16x+64)-27=0
3(x2-16x+64)-27=0
Step 2.1.1.4
Apply the distributive property.
3x2+3(-16x)+364-27=0
Step 2.1.1.5
Simplify.
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Step 2.1.1.5.1
Multiply -16 by 3.
3x2-48x+364-27=0
Step 2.1.1.5.2
Multiply 3 by 64.
3x2-48x+192-27=0
3x2-48x+192-27=0
3x2-48x+192-27=0
Step 2.1.2
Subtract 27 from 192.
3x2-48x+165=0
3x2-48x+165=0
Step 2.2
Graph each side of the equation. The solution is the x-value of the point of intersection.
x=5,11
x=5,11
Step 3
image of graph
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