# Solve using the Square Root Property x^2-11x-21=0

x2-11x-21=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-11, and c=-21 into the quadratic formula and solve for x.
11±(-11)2-4⋅(1⋅-21)2⋅1
Simplify.
Simplify the numerator.
Raise -11 to the power of 2.
x=11±121-4⋅(1⋅-21)2⋅1
Multiply -21 by 1.
x=11±121-4⋅-212⋅1
Multiply -4 by -21.
x=11±121+842⋅1
x=11±2052⋅1
x=11±2052⋅1
Multiply 2 by 1.
x=11±2052
x=11±2052
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -11 to the power of 2.
x=11±121-4⋅(1⋅-21)2⋅1
Multiply -21 by 1.
x=11±121-4⋅-212⋅1
Multiply -4 by -21.
x=11±121+842⋅1
x=11±2052⋅1
x=11±2052⋅1
Multiply 2 by 1.
x=11±2052
Change the ± to +.
x=11+2052
x=11+2052
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -11 to the power of 2.
x=11±121-4⋅(1⋅-21)2⋅1
Multiply -21 by 1.
x=11±121-4⋅-212⋅1
Multiply -4 by -21.
x=11±121+842⋅1
x=11±2052⋅1
x=11±2052⋅1
Multiply 2 by 1.
x=11±2052
Change the ± to -.
x=11-2052
x=11-2052
The final answer is the combination of both solutions.
x=11+2052,11-2052
The result can be shown in multiple forms.
Exact Form:
x=11+2052,11-2052
Decimal Form:
x=12.65891053…,-1.65891053…
Solve using the Square Root Property x^2-11x-21=0