Solve for x -3(100x^2-49)(x^2-2)=0

$- 3 (100 x^{2} - 49) (x^{2} - 2) = 0$

Step 1

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

$100 x^{2} - 49 = 0$

$x^{2} - 2 = 0$

Step 2

Set $100 x^{2} - 49$ equal to $0$ and solve for $x$ .

Set $100 x^{2} - 49$ equal to $0$ .

$100 x^{2} - 49 = 0$

Solve $100 x^{2} - 49 = 0$ for $x$ .

Add $49$ to both sides of the equation.

$100 x^{2} = 49$

Divide each term in $100 x^{2} = 49$ by $100$ and simplify.

Divide each term in $100 x^{2} = 49$ by $100$ .

$\frac{100 x^{2}}{100} = \frac{49}{100}$

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$\frac{100 x^{2}}{100} = \frac{49}{100}$

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

$x^{2} = \frac{49}{100}$

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

$x = \pm \sqrt{\frac{49}{100}}$

Simplify $\pm \sqrt{\frac{49}{100}}$ .

Rewrite $\sqrt{\frac{49}{100}}$ as $\frac{\sqrt{49}}{\sqrt{100}}$ .

$x = \pm \frac{\sqrt{49}}{\sqrt{100}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{7^{2}}}{\sqrt{100}}$

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

$x = \pm \frac{7}{\sqrt{100}}$

Simplify the denominator.

Rewrite $100$ as $10^{2}$ .

$x = \pm \frac{7}{\sqrt{10^{2}}}$

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

$x = \pm \frac{7}{10}$

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.

$x = \frac{7}{10}$

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

$x = - \frac{7}{10}$

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

$x = \frac{7}{10}, - \frac{7}{10}$

Step 3

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

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

$x^{2} - 2 = 0$

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

Add $2$ to both sides of the equation.

$x^{2} = 2$

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

$x = \pm \sqrt{2}$

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.

$x = \sqrt{2}$

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

$x = - \sqrt{2}$

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

$x = \sqrt{2}, - \sqrt{2}$

Step 4

The final solution is all the values that make $- 3 (100 x^{2} - 49) (x^{2} - 2) = 0$ true.

$x = \frac{7}{10}, - \frac{7}{10}, \sqrt{2}, - \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{10}, - \frac{7}{10}, \sqrt{2}, - \sqrt{2}$

Decimal Form:

$x = 0.7, - 0.7, 1.41421356 \dots, - 1.41421356 \dots$

Solve for x -3(100x^2-49)(x^2-2)=0

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