Solve for x 9(x^2-10)-3=7

$9 (x^{2} - 10) - 3 = 7$

Simplify $9 (x^{2} - 10) - 3$ .

Simplify each term.

Apply the distributive property.

$9 x^{2} + 9 \cdot - 10 - 3 = 7$

Multiply $9$ by $- 10$ .

$9 x^{2} - 90 - 3 = 7$

Subtract $3$ from $- 90$ .

$9 x^{2} - 93 = 7$

Move all terms not containing $x$ to the right side of the equation.

Add $93$ to both sides of the equation.

$9 x^{2} = 7 + 93$

Add $7$ and $93$ .

$9 x^{2} = 100$

Divide each term in $9 x^{2} = 100$ by $9$ and simplify.

Divide each term in $9 x^{2} = 100$ by $9$ .

$\frac{9 x^{2}}{9} = \frac{100}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x^{2}}{9} = \frac{100}{9}$

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

$x^{2} = \frac{100}{9}$

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

$x = \pm \sqrt{\frac{100}{9}}$

Simplify $\pm \sqrt{\frac{100}{9}}$ .

Rewrite $\sqrt{\frac{100}{9}}$ as $\frac{\sqrt{100}}{\sqrt{9}}$ .

$x = \pm \frac{\sqrt{100}}{\sqrt{9}}$

Simplify the numerator.

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

$x = \pm \frac{\sqrt{10^{2}}}{\sqrt{9}}$

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

$x = \pm \frac{10}{\sqrt{9}}$

Simplify the denominator.

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

$x = \pm \frac{10}{\sqrt{3^{2}}}$

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

$x = \pm \frac{10}{3}$

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.

$x = \frac{10}{3}$

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

$x = - \frac{10}{3}$

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

$x = \frac{10}{3}, - \frac{10}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10}{3}, - \frac{10}{3}$

Decimal Form:

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

Mixed Number Form:

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

Solve for x 9(x^2-10)-3=7

Related Questions

Support LCMGCF.com by disabling your adblocker.