# Solve Using the Square Root Property x(x-3)=9

x(x-3)=9
Simplify x(x-3).
Apply the distributive property.
x⋅x+x⋅-3=9
Simplify the expression.
Multiply x by x.
x2+x⋅-3=9
Move -3 to the left of x.
x2-3x=9
x2-3x=9
x2-3x=9
Move 9 to the left side of the equation by subtracting it from both sides.
x2-3x-9=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-3, and c=-9 into the quadratic formula and solve for x.
3±(-3)2-4⋅(1⋅-9)2⋅1
Simplify.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅-9)2⋅1
Multiply -9 by 1.
x=3±9-4⋅-92⋅1
Multiply -4 by -9.
x=3±9+362⋅1
Add 9 and 36.
x=3±452⋅1
Rewrite 45 as 32⋅5.
Factor 9 out of 45.
x=3±9(5)2⋅1
Rewrite 9 as 32.
x=3±32⋅52⋅1
x=3±32⋅52⋅1
Pull terms out from under the radical.
x=3±352⋅1
x=3±352⋅1
Multiply 2 by 1.
x=3±352
x=3±352
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅-9)2⋅1
Multiply -9 by 1.
x=3±9-4⋅-92⋅1
Multiply -4 by -9.
x=3±9+362⋅1
Add 9 and 36.
x=3±452⋅1
Rewrite 45 as 32⋅5.
Factor 9 out of 45.
x=3±9(5)2⋅1
Rewrite 9 as 32.
x=3±32⋅52⋅1
x=3±32⋅52⋅1
Pull terms out from under the radical.
x=3±352⋅1
x=3±352⋅1
Multiply 2 by 1.
x=3±352
Change the ± to +.
x=3+352
x=3+352
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅-9)2⋅1
Multiply -9 by 1.
x=3±9-4⋅-92⋅1
Multiply -4 by -9.
x=3±9+362⋅1
Add 9 and 36.
x=3±452⋅1
Rewrite 45 as 32⋅5.
Factor 9 out of 45.
x=3±9(5)2⋅1
Rewrite 9 as 32.
x=3±32⋅52⋅1
x=3±32⋅52⋅1
Pull terms out from under the radical.
x=3±352⋅1
x=3±352⋅1
Multiply 2 by 1.
x=3±352
Change the ± to -.
x=3-352
x=3-352
The final answer is the combination of both solutions.
x=3+352,3-352
The result can be shown in multiple forms.
Exact Form:
x=3+352,3-352
Decimal Form:
x=4.85410196…,-1.85410196…
Solve Using the Square Root Property x(x-3)=9

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