Question
Simplify the expression
441x4−336x2+64
Evaluate
(7x2×3−8)2
Multiply the terms
(21x2−8)2
Use (a−b)2=a2−2ab+b2 to expand the expression
(21x2)2−2×21x2×8+82
Solution
441x4−336x2+64
Show Solution

Find the roots
x1=−21242,x2=21242
Alternative Form
x1≈−0.617213,x2≈0.617213
Evaluate
(7x2×3−8)2
To find the roots of the expression,set the expression equal to 0
(7x2×3−8)2=0
Multiply the terms
(21x2−8)2=0
The only way a power can be 0 is when the base equals 0
21x2−8=0
Move the constant to the right-hand side and change its sign
21x2=0+8
Removing 0 doesn't change the value,so remove it from the expression
21x2=8
Divide both sides
2121x2=218
Divide the numbers
x2=218
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±218
Simplify the expression
More Steps

Evaluate
218
To take a root of a fraction,take the root of the numerator and denominator separately
218
Simplify the radical expression
More Steps

Evaluate
8
Write the expression as a product where the root of one of the factors can be evaluated
4×2
Write the number in exponential form with the base of 2
22×2
The root of a product is equal to the product of the roots of each factor
22×2
Reduce the index of the radical and exponent with 2
22
2122
Multiply by the Conjugate
21×2122×21
Multiply the numbers
More Steps

Evaluate
2×21
The product of roots with the same index is equal to the root of the product
2×21
Calculate the product
42
21×21242
When a square root of an expression is multiplied by itself,the result is that expression
21242
x=±21242
Separate the equation into 2 possible cases
x=21242x=−21242
Solution
x1=−21242,x2=21242
Alternative Form
x1≈−0.617213,x2≈0.617213
Show Solution
