# Solve Using the Square Root Property x^2-6x=10^2 x2-6x=102
Raise 10 to the power of 2.
x2-6x=100
Move 100 to the left side of the equation by subtracting it from both sides.
x2-6x-100=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-6, and c=-100 into the quadratic formula and solve for x.
6±(-6)2-4⋅(1⋅-100)2⋅1
Simplify.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-100)2⋅1
Multiply -100 by 1.
x=6±36-4⋅-1002⋅1
Multiply -4 by -100.
x=6±36+4002⋅1
x=6±4362⋅1
Rewrite 436 as 22⋅109.
Factor 4 out of 436.
x=6±4(109)2⋅1
Rewrite 4 as 22.
x=6±22⋅1092⋅1
x=6±22⋅1092⋅1
Pull terms out from under the radical.
x=6±21092⋅1
x=6±21092⋅1
Multiply 2 by 1.
x=6±21092
Simplify 6±21092.
x=3±109
x=3±109
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-100)2⋅1
Multiply -100 by 1.
x=6±36-4⋅-1002⋅1
Multiply -4 by -100.
x=6±36+4002⋅1
x=6±4362⋅1
Rewrite 436 as 22⋅109.
Factor 4 out of 436.
x=6±4(109)2⋅1
Rewrite 4 as 22.
x=6±22⋅1092⋅1
x=6±22⋅1092⋅1
Pull terms out from under the radical.
x=6±21092⋅1
x=6±21092⋅1
Multiply 2 by 1.
x=6±21092
Simplify 6±21092.
x=3±109
Change the ± to +.
x=3+109
x=3+109
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-100)2⋅1
Multiply -100 by 1.
x=6±36-4⋅-1002⋅1
Multiply -4 by -100.
x=6±36+4002⋅1
x=6±4362⋅1
Rewrite 436 as 22⋅109.
Factor 4 out of 436.
x=6±4(109)2⋅1
Rewrite 4 as 22.
x=6±22⋅1092⋅1
x=6±22⋅1092⋅1
Pull terms out from under the radical.
x=6±21092⋅1
x=6±21092⋅1
Multiply 2 by 1.
x=6±21092
Simplify 6±21092.
x=3±109
Change the ± to -.
x=3-109
x=3-109
The final answer is the combination of both solutions.
x=3+109,3-109
The result can be shown in multiple forms.
Exact Form:
x=3+109,3-109
Decimal Form:
x=13.44030650…,-7.44030650…
Solve Using the Square Root Property x^2-6x=10^2     