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

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.
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
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 expression to solve for the + portion of the ±.
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
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 expression to solve for the – portion of the ±.
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
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