Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4−x2
Evaluate
22−x2
Solution
4−x2
Show Solution
Find the roots
x1=−2,x2=2
Evaluate
22−x2
To find the roots of the expression,set the expression equal to 0
22−x2=0
Find the domain
More Steps
Evaluate
22−x2≥0
Evaluate the power
4−x2≥0
Rewrite the expression
−x2≥−4
Change the signs on both sides of the inequality and flip the inequality sign
x2≤4
Take the 2-th root on both sides of the inequality
x2≤4
Calculate
∣x∣≤2
Separate the inequality into 2 possible cases
{x≤2x≥−2
Find the intersection
−2≤x≤2
22−x2=0,−2≤x≤2
Calculate
22−x2=0
Evaluate the power
4−x2=0
The only way a root could be 0 is when the radicand equals 0
4−x2=0
Move the constant to the right-hand side and change its sign
−x2=0−4
Removing 0 doesn't change the value,so remove it from the expression
−x2=−4
Change the signs on both sides of the equation
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
x=±2
Separate the equation into 2 possible cases
x=2x=−2
Check if the solution is in the defined range
x=2x=−2,−2≤x≤2
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
Show Solution