How do you solve the equation for #x^2 - 3x = 0#?

Answer 1
#x^2 - 3x = 0#
# x*(x-3) = 0 # (#x# was a common factor to both the terms)
In general, if #a*b = 0,# then either # a = 0 or b = 0#
So here, # x = 0 or x - 3 = 0# # color(green)( x = 0 or x = 3# is the correct Solution.
#color(red)(Note# :
Here's a classic #color(red)(Mistake# that many students make:
Transpose #3x# to the right hand side
#x^2 = 3x #
Divide both sides by #x# will give us #x = 3# (Incorrect/Incomplete)
This is a #color(red)(mistake# because we CANNOT divide by #x# unless we are sure about it not being equal to zero.
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Answer 2
To find #x#, we first have to factorize the equation. #x^2-3x=0# As #x# is the common factor between the 2 values, we factorize the equation by taking #x# out of #x^2-3x=0#
#x^2-3x=0# #x(x-3)=0#

Any value that is multiplied by 0, will give 0 as the answer. 1x0=0 2x0=0 3x0=0

From here, we know that in #x(x-3)=0#, #x=0# and #(x-3)=0#
#(x-3)=0# #x=3#
Therefore #x=0# and #x=3#
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Answer 3

To solve the equation x^2 - 3x = 0:

  1. Factor out x from both terms: x(x - 3) = 0

  2. Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero. Set each factor equal to zero: a) x = 0 b) x - 3 = 0

  3. Solve for x in each equation: a) x = 0 b) x - 3 = 0 x = 3

  4. The solutions to the equation x^2 - 3x = 0 are x = 0 and x = 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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