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# Find the Mistake in Solving a Quadratic Equation

GRE-WK8GX4

Sam solved the following equation for $x$. Find the line that has a mistake or state that there is no mistake:

Equation: $8{ x }^{ 2 }(3x+7)+2x=24{ x }^{ 3 }+50{ x }^{ 2 }$

Step 1: $24{ x }^{ 3 }+56{ x }^{ 2 }+2x=24{ x }^{ 3 }+50{ x }^{ 2 }$
Step 2: $56{ x }^{ 2 }+2x=50{ x }^{ 2 }$
Step 3: $6{ x }^{ 2 }+2x=0$
Step 4: $2x(3x+1)=0$
Step 5: $3x+1=0$
Step 6: $3x=-1$
Step 7: $x=-\cfrac { 1 }{ 3 }$

A

Step 2

B

Step 3

C

Step 4

D

Step 5

E

Step 7

F

There is no mistake.