Solve for x -2(x^2-25)(9x^2-49)=0

$- 2 (x^{2} - 25) (9 x^{2} - 49) = 0$

Step 1

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

$x^{2} - 25 = 0$

$9 x^{2} - 49 = 0$

Step 2

Set $x^{2} - 25$ equal to $0$ and solve for $x$ .

Set $x^{2} - 25$ equal to $0$ .

$x^{2} - 25 = 0$

Solve $x^{2} - 25 = 0$ for $x$ .

Add $25$ to both sides of the equation.

$x^{2} = 25$

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

$x = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x = \pm \sqrt{5^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 5$

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.

$x = 5$

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

$x = - 5$

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

$x = 5, - 5$

Step 3

Set $9 x^{2} - 49$ equal to $0$ and solve for $x$ .

Set $9 x^{2} - 49$ equal to $0$ .

$9 x^{2} - 49 = 0$

Solve $9 x^{2} - 49 = 0$ for $x$ .

Add $49$ to both sides of the equation.

$9 x^{2} = 49$

Divide each term in $9 x^{2} = 49$ by $9$ and simplify.

Divide each term in $9 x^{2} = 49$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{49}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{49}{9}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{49}{9}$

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

$x = \pm \sqrt{\frac{49}{9}}$

Simplify $\pm \sqrt{\frac{49}{9}}$ .

Rewrite $\sqrt{\frac{49}{9}}$ as $\frac{\sqrt{49}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{9}}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{9}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{7}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$x = \pm \frac{7}{\sqrt{3^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm \frac{7}{3}$

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.

$x = \frac{7}{3}$

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

$x = - \frac{7}{3}$

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

$x = \frac{7}{3}, - \frac{7}{3}$

Step 4

The final solution is all the values that make $- 2 (x^{2} - 25) (9 x^{2} - 49) = 0$ true.

$x = 5, - 5, \frac{7}{3}, - \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 5, - 5, \frac{7}{3}, - \frac{7}{3}$

Decimal Form:

$x = 5, - 5, 2.\overline{3}, - 2.\overline{3}$

Mixed Number Form:

$x = 5, - 5, 2 \frac{1}{3}, - 2 \frac{1}{3}$

Solve for x -2(x^2-25)(9x^2-49)=0

Related Questions

Support LCMGCF.com by disabling your adblocker.