How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11