Solve for x (8x+9)(49x^2-100)=0

$(8 x + 9) (49 x^{2} - 100) = 0$

Step 1

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

$8 x + 9 = 0$

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

Step 2

Set $8 x + 9$ equal to $0$ and solve for $x$ .

Set $8 x + 9$ equal to $0$ .

$8 x + 9 = 0$

Solve $8 x + 9 = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$8 x = - 9$

Divide each term in $8 x = - 9$ by $8$ and simplify.

Divide each term in $8 x = - 9$ by $8$ .

$\frac{8 x}{8} = \frac{- 9}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 9}{8}$

Divide $x$ by $1$ .

$x = \frac{- 9}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{8}$

Step 3

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

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

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

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

Add $100$ to both sides of the equation.

$49 x^{2} = 100$

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

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

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

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

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

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

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

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

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

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

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

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

Simplify the numerator.

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

$x = \pm \frac{\sqrt{10^{2}}}{\sqrt{49}}$

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

$x = \pm \frac{10}{\sqrt{49}}$

Simplify the denominator.

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

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

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

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

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.

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

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

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

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

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

Step 4

The final solution is all the values that make $(8 x + 9) (49 x^{2} - 100) = 0$ true.

$x = - \frac{9}{8}, \frac{10}{7}, - \frac{10}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9}{8}, \frac{10}{7}, - \frac{10}{7}$

Decimal Form:

$x = - 1.125, 1.\overline{428571}, - 1.\overline{428571}$

Mixed Number Form:

$x = - 1 \frac{1}{8}, 1 \frac{3}{7}, - 1 \frac{3}{7}$

Solve for x (8x+9)(49x^2-100)=0

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