Solve for x (8x-1)(x^2-15)=0

$(8 x - 1) (x^{2} - 15) = 0$

Step 1

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

$8 x - 1 = 0$

$x^{2} - 15 = 0$

Step 2

Set $8 x - 1$ equal to $0$ and solve for $x$ .

Set $8 x - 1$ equal to $0$ .

$8 x - 1 = 0$

Solve $8 x - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$8 x = 1$

Divide each term in $8 x = 1$ by $8$ and simplify.

Divide each term in $8 x = 1$ by $8$ .

$\frac{8 x}{8} = \frac{1}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{1}{8}$

Divide $x$ by $1$ .

$x = \frac{1}{8}$

Step 3

Set $x^{2} - 15$ equal to $0$ and solve for $x$ .

Set $x^{2} - 15$ equal to $0$ .

$x^{2} - 15 = 0$

Solve $x^{2} - 15 = 0$ for $x$ .

Add $15$ to both sides of the equation.

$x^{2} = 15$

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

$x = \pm \sqrt{15}$

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.

$x = \sqrt{15}$

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

$x = - \sqrt{15}$

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

$x = \sqrt{15}, - \sqrt{15}$

Step 4

The final solution is all the values that make $(8 x - 1) (x^{2} - 15) = 0$ true.

$x = \frac{1}{8}, \sqrt{15}, - \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{8}, \sqrt{15}, - \sqrt{15}$

Decimal Form:

$x = 0.125, 3.87298334 \dots, - 3.87298334 \dots$

Solve for x (8x-1)(x^2-15)=0

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