Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x25x4−20
Evaluate
5x2−x220
Reduce fractions to a common denominator
x25x2×x2−x220
Write all numerators above the common denominator
x25x2×x2−20
Solution
More Steps
Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
x25x4−20
Show Solution
Find the excluded values
x=0
Evaluate
5x2−x220
To find the excluded values,set the denominators equal to 0
x2=0
Solution
x=0
Show Solution
Find the roots
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Evaluate
5x2−x220
To find the roots of the expression,set the expression equal to 0
5x2−x220=0
The only way a power can not be 0 is when the base not equals 0
5x2−x220=0,x=0
Calculate
5x2−x220=0
Subtract the terms
More Steps
Simplify
5x2−x220
Reduce fractions to a common denominator
x25x2×x2−x220
Write all numerators above the common denominator
x25x2×x2−20
Multiply the terms
More Steps
Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
x25x4−20
x25x4−20=0
Cross multiply
5x4−20=x2×0
Simplify the equation
5x4−20=0
Move the constant to the right side
5x4=20
Divide both sides
55x4=520
Divide the numbers
x4=520
Divide the numbers
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Evaluate
520
Reduce the numbers
14
Calculate
4
x4=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±44
Simplify the expression
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Evaluate
44
Write the number in exponential form with the base of 2
422
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,x=0
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Show Solution