Rewrite <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Let <math><mstyle displaystyle="true"><mi>u</mi><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> . Substitute <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> for all occurrences of <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>7</mn></mstyle></math> .

Write the factored form using these integers.

Replace all occurrences of <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> with <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Since both terms are perfect squares, factor using the difference of squares formula, <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></mrow></mstyle></math> where <math><mstyle displaystyle="true"><mi>a</mi><mo>=</mo><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi><mo>=</mo><mn>1</mn></mstyle></math> .

Remove unnecessary parentheses.

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set the first factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> 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.

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> 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 <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from both sides of the equation.

Set the next factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

The final solution is all the values that make <math><mstyle displaystyle="true"><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>6</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Do you know how to Solve by Factoring x^4-7x^2+6=0? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name | two hundred sixty-one million two hundred fifty-one thousand three hundred fifty-three |
---|

- 261251353 has 16 divisors, whose sum is
**295764480** - The reverse of 261251353 is
**353152162** - Previous prime number is
**197**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 28
- Digital Root 1

Name | two hundred thirty-five million two hundred thirty-one thousand four hundred fifty-eight |
---|

- 235231458 has 128 divisors, whose sum is
**766181376** - The reverse of 235231458 is
**854132532** - Previous prime number is
**7**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 33
- Digital Root 6

Name | five hundred one million five hundred ninety-five thousand nine hundred forty-one |
---|

- 501595941 has 32 divisors, whose sum is
**628379136** - The reverse of 501595941 is
**149595105** - Previous prime number is
**307**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 39
- Digital Root 3