x(x-3)=9

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 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 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 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