Find the Roots (Zeros) 0=x^3+9x^2-7x-63

$0 = x^{3} + 9 x^{2} - 7 x - 63$

Rewrite the equation as $x^{3} + 9 x^{2} - 7 x - 63 = 0$ .

$x^{3} + 9 x^{2} - 7 x - 63 = 0$

Factor the left side of the equation.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(x^{3} + 9 x^{2}) - 7 x - 63 = 0$

Factor out the greatest common factor (GCF) from each group.

$x^{2} (x + 9) - 7 (x + 9) = 0$

Factor the polynomial by factoring out the greatest common factor, $x + 9$ .

$(x + 9) (x^{2} - 7) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 9 = 0$

$x^{2} - 7 = 0$

Set $x + 9$ equal to $0$ and solve for $x$ .

Set $x + 9$ equal to $0$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

Set $x^{2} - 7$ equal to $0$ and solve for $x$ .

Set $x^{2} - 7$ equal to $0$ .

$x^{2} - 7 = 0$

Solve $x^{2} - 7 = 0$ for $x$ .

Add $7$ to both sides of the equation.

$x^{2} = 7$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{7}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{7}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{7}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{7}, - \sqrt{7}$

The final solution is all the values that make $(x + 9) (x^{2} - 7) = 0$ true.

$x = - 9, \sqrt{7}, - \sqrt{7}$

The result can be shown in multiple forms.

Exact Form:

$x = - 9, \sqrt{7}, - \sqrt{7}$

Decimal Form:

$x = - 9, 2.64575131 \dots, - 2.64575131 \dots$