Solve by Factoring x^4-7x^2+6=0

Solve by Factoring x^4-7x^2+6=0
Rewrite as .
Let . Substitute for all occurrences of .
Factor using the AC method.
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Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Replace all occurrences of with .
Rewrite as .
Factor.
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Since both terms are perfect squares, factor using the difference of squares formula, where and .
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
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Set the first factor equal to .
Add to both sides of the equation.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Set the next factor equal to and solve.
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Set the next factor equal to .
Subtract from both sides of the equation.
Set the next factor equal to and solve.
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Set the next factor equal to .
Add to both sides of the equation.
The final solution is all the values that make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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Name

Name five hundred eighty-seven million six hundred ninety-eight thousand six hundred seventy-two

Interesting facts

  • 587698672 has 128 divisors, whose sum is 3269185920
  • The reverse of 587698672 is 276896785
  • Previous prime number is 139

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 58
  • Digital Root 4

Name

Name one billion two hundred ninety-nine million nine hundred seventy-four thousand seven hundred thirteen

Interesting facts

  • 1299974713 has 16 divisors, whose sum is 1336787712
  • The reverse of 1299974713 is 3174799921
  • Previous prime number is 311

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 52
  • Digital Root 7

Name

Name one billion eight hundred fifty-two million eighty-four thousand sixty-nine

Interesting facts

  • 1852084069 has 8 divisors, whose sum is 2023737408
  • The reverse of 1852084069 is 9604802581
  • Previous prime number is 617

Basic properties

  • Is Prime? no
  • Number parity odd
  • Number length 10
  • Sum of Digits 43
  • Digital Root 7