Solve for x -4/3x^2-15=201

$- \frac{4}{3} x^{2} - 15 = 201$

Step 1

Simplify each term.

Combine $x^{2}$ and $\frac{4}{3}$ .

$- \frac{x^{2} \cdot 4}{3} - 15 = 201$

Move $4$ to the left of $x^{2}$ .

$- \frac{4 x^{2}}{3} - 15 = 201$

Step 2

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

Add $15$ to both sides of the equation.

$- \frac{4 x^{2}}{3} = 201 + 15$

Add $201$ and $15$ .

$- \frac{4 x^{2}}{3} = 216$

Step 3

Multiply both sides of the equation by $- \frac{3}{4}$ .

$- \frac{3}{4} (- \frac{4 x^{2}}{3}) = - \frac{3}{4} \cdot 216$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{4} (- \frac{4 x^{2}}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 x^{2}}{3}) = - \frac{3}{4} \cdot 216$

Move the leading negative in $- \frac{4 x^{2}}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 x^{2}}{3} = - \frac{3}{4} \cdot 216$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 x^{2}}{3} = - \frac{3}{4} \cdot 216$

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 x^{2}}{3} = - \frac{3}{4} \cdot 216$

Rewrite the expression.

$\frac{- 1}{4} (- 4 x^{2}) = - \frac{3}{4} \cdot 216$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 x^{2}$ .

$\frac{- 1}{4} (4 (- x^{2})) = - \frac{3}{4} \cdot 216$

Cancel the common factor.

$\frac{- 1}{4} (4 (- x^{2})) = - \frac{3}{4} \cdot 216$

Rewrite the expression.

$- - x^{2} = - \frac{3}{4} \cdot 216$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x^{2} = - \frac{3}{4} \cdot 216$

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

$x^{2} = - \frac{3}{4} \cdot 216$

Simplify the right side.

Simplify $- \frac{3}{4} \cdot 216$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$x^{2} = \frac{- 3}{4} \cdot 216$

Factor $4$ out of $216$ .

$x^{2} = \frac{- 3}{4} \cdot (4 (54))$

Cancel the common factor.

$x^{2} = \frac{- 3}{4} \cdot (4 \cdot 54)$

Rewrite the expression.

$x^{2} = - 3 \cdot 54$

Multiply $- 3$ by $54$ .

$x^{2} = - 162$

Step 5

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

$x = \pm \sqrt{- 162}$

Step 6

Simplify $\pm \sqrt{- 162}$ .

Rewrite $- 162$ as $- 1 (162)$ .

$x = \pm \sqrt{- 1 (162)}$

Rewrite $\sqrt{- 1 (162)}$ as $\sqrt{- 1} \cdot \sqrt{162}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{162}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{162}$

Rewrite $162$ as $9^{2} \cdot 2$ .

Factor $81$ out of $162$ .

$x = \pm i \cdot \sqrt{81 (2)}$

Rewrite $81$ as $9^{2}$ .

$x = \pm i \cdot \sqrt{9^{2} \cdot 2}$

Pull terms out from under the radical.

$x = \pm i \cdot (9 \sqrt{2})$

Move $9$ to the left of $i$ .

$x = \pm 9 i \sqrt{2}$

Step 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.

$x = 9 i \sqrt{2}$

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

$x = - 9 i \sqrt{2}$

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

$x = 9 i \sqrt{2}, - 9 i \sqrt{2}$

Solve for x -4/3x^2-15=201

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