# Taking a Square Root to Solve an Equation ```Taking a Square Root to Solve
an Equation
Taking a Square Root to Solve an
Equation
Solve:
What are the
number(s)
whose square
is 9?
Find the x
that makes
x-7 equal
POSITIVE 3
 x  7
9
x7   9
x  7  3
2
In order to solve for x,
you have to UNDO the
squared first (i.e. square
root)
The square
of 3 AND -3
is 9
x  7  3 x  7  3
x  10
x4
Find the x
that makes
x-7 equal
NEGATIVE 3
NOTE: In general, this method only works when
there is ONE variable in the equation.
Taking a Square Root to Solve an
Equation
 x  3
 12
x  3   12
x  3  2 3
Solve:
What are the
number(s)
whose square
is 12?
2
Simplify any
square roots
In order to solve for x,
you have to UNDO the
squared first (i.e. square
root)
Do not forget the square of
a positive and negative
number is positive
x  3  2 3 x  3  2 3
Find the x
that makes
x-3 equal a
POSITIVE
x  3 2 3 x  3 2 3
Find the x
that makes
x-3 equal a
NEGATIVE
x  3 2 3
x  0.464 or 6.464
Is also an acceptable EXACT answer
Taking a Square Root to Solve an
Equation
Solve:
What are the
number(s)
whose square
is -11?
 x  2
 11
x  2   11
2
In order to solve for x,
you have to UNDO the
squared first (i.e. square
root)
NOT POSSIBLE
The square of a number can not be negative.
This equation has NO SOLUTIONS.
Taking a Square Root to Solve an
Equation
Solve:
What are the
number(s)
whose square
is 0?
Since +0 and
-0 are the
same
number.
There is only
ONE
 5  10 x 
0
5  10x   0
5 10 x  0
2
5  10 x  0
10 x  5
x  12
In order to solve for x,
you have to UNDO the
squared first (i.e. square
root)
The square
of 0 AND -0
is 0
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