Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2x4−x2
Evaluate
x2−21x
Rewrite the expression
x2−2x
Reduce fractions to a common denominator
x×22×2−2xx×x
Use the commutative property to reorder the terms
2x2×2−2xx×x
Write all numerators above the common denominator
2x2×2−x×x
Multiply the numbers
2x4−x×x
Solution
2x4−x2
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Find the excluded values
x=0
Evaluate
x2−21x
Solution
x=0
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Find the roots
x1=−2,x2=2
Evaluate
x2−21x
To find the roots of the expression,set the expression equal to 0
x2−21x=0
Find the domain
x2−21x=0,x=0
Calculate
x2−21x=0
Subtract the terms
More Steps
Simplify
x2−21x
Rewrite the expression
x2−2x
Reduce fractions to a common denominator
x×22×2−2xx×x
Use the commutative property to reorder the terms
2x2×2−2xx×x
Write all numerators above the common denominator
2x2×2−x×x
Multiply the numbers
2x4−x×x
Multiply the terms
2x4−x2
2x4−x2=0
Cross multiply
4−x2=2x×0
Simplify the equation
4−x2=0
Rewrite 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,x=0
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
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