x2-5x=5

Move 5 to the left side of the equation by subtracting it from both sides.

x2-5x-5=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=-5, and c=-5 into the quadratic formula and solve for x.

5±(-5)2-4⋅(1⋅-5)2⋅1

Simplify the numerator.

Raise -5 to the power of 2.

x=5±25-4⋅(1⋅-5)2⋅1

Multiply -5 by 1.

x=5±25-4⋅-52⋅1

Multiply -4 by -5.

x=5±25+202⋅1

Add 25 and 20.

x=5±452⋅1

Rewrite 45 as 32⋅5.

Factor 9 out of 45.

x=5±9(5)2⋅1

Rewrite 9 as 32.

x=5±32⋅52⋅1

x=5±32⋅52⋅1

Pull terms out from under the radical.

x=5±352⋅1

x=5±352⋅1

Multiply 2 by 1.

x=5±352

x=5±352

Simplify the numerator.

Raise -5 to the power of 2.

x=5±25-4⋅(1⋅-5)2⋅1

Multiply -5 by 1.

x=5±25-4⋅-52⋅1

Multiply -4 by -5.

x=5±25+202⋅1

Add 25 and 20.

x=5±452⋅1

Rewrite 45 as 32⋅5.

Factor 9 out of 45.

x=5±9(5)2⋅1

Rewrite 9 as 32.

x=5±32⋅52⋅1

x=5±32⋅52⋅1

Pull terms out from under the radical.

x=5±352⋅1

x=5±352⋅1

Multiply 2 by 1.

x=5±352

Change the ± to +.

x=5+352

x=5+352

Simplify the numerator.

Raise -5 to the power of 2.

x=5±25-4⋅(1⋅-5)2⋅1

Multiply -5 by 1.

x=5±25-4⋅-52⋅1

Multiply -4 by -5.

x=5±25+202⋅1

Add 25 and 20.

x=5±452⋅1

Rewrite 45 as 32⋅5.

Factor 9 out of 45.

x=5±9(5)2⋅1

Rewrite 9 as 32.

x=5±32⋅52⋅1

x=5±32⋅52⋅1

Pull terms out from under the radical.

x=5±352⋅1

x=5±352⋅1

Multiply 2 by 1.

x=5±352

Change the ± to -.

x=5-352

x=5-352

The final answer is the combination of both solutions.

x=5+352,5-352

The result can be shown in multiple forms.

Exact Form:

x=5+352,5-352

Decimal Form:

x=5.85410196…,-0.85410196…

Solve Using the Square Root Property x^2-5x=5