Solve Using the Quadratic Formula -4/3x^2-15=201

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

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify each term.

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

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

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

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

Subtract $201$ from both sides of the equation.

$- \frac{4 x^{2}}{3} - 15 - 201 = 0$

Subtract $201$ from $- 15$ .

$- \frac{4 x^{2}}{3} - 216 = 0$

Step 2

Multiply through by the least common denominator $3$ , then simplify.

Apply the distributive property.

$3 (- \frac{4 x^{2}}{3}) + 3 \cdot - 216 = 0$

Cancel the common factor of $3$ .

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

$3 (\frac{- 4 x^{2}}{3}) + 3 \cdot - 216 = 0$

Cancel the common factor.

$3 (\frac{- 4 x^{2}}{3}) + 3 \cdot - 216 = 0$

Rewrite the expression.

$- 4 x^{2} + 3 \cdot - 216 = 0$

Multiply $3$ by $- 216$ .

$- 4 x^{2} - 648 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 4$ , $b = 0$ , and $c = - 648$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 4 \cdot - 648)}}{2 \cdot - 4}$

Step 5

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 4 \cdot - 648}}{2 \cdot - 4}$

Multiply $- 4 \cdot - 4 \cdot - 648$ .

Multiply $- 4$ by $- 4$ .

$x = \frac{0 \pm \sqrt{0 + 16 \cdot - 648}}{2 \cdot - 4}$

Multiply $16$ by $- 648$ .

$x = \frac{0 \pm \sqrt{0 - 10368}}{2 \cdot - 4}$

Subtract $10368$ from $0$ .

$x = \frac{0 \pm \sqrt{- 10368}}{2 \cdot - 4}$

Rewrite $- 10368$ as $- 1 (10368)$ .

$x = \frac{0 \pm \sqrt{- 1 \cdot 10368}}{2 \cdot - 4}$

Rewrite $\sqrt{- 1 (10368)}$ as $\sqrt{- 1} \cdot \sqrt{10368}$ .

$x = \frac{0 \pm \sqrt{- 1} \cdot \sqrt{10368}}{2 \cdot - 4}$

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

$x = \frac{0 \pm i \cdot \sqrt{10368}}{2 \cdot - 4}$

Rewrite $10368$ as $72^{2} \cdot 2$ .

Factor $5184$ out of $10368$ .

$x = \frac{0 \pm i \cdot \sqrt{5184 (2)}}{2 \cdot - 4}$

Rewrite $5184$ as $72^{2}$ .

$x = \frac{0 \pm i \cdot \sqrt{72^{2} \cdot 2}}{2 \cdot - 4}$

Pull terms out from under the radical.

$x = \frac{0 \pm i \cdot (72 \sqrt{2})}{2 \cdot - 4}$

Move $72$ to the left of $i$ .

$x = \frac{0 \pm 72 i \sqrt{2}}{2 \cdot - 4}$

Multiply $2$ by $- 4$ .

$x = \frac{0 \pm 72 i \sqrt{2}}{- 8}$

Simplify $\frac{0 \pm 72 i \sqrt{2}}{- 8}$ .

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

Solve Using the Quadratic Formula -4/3x^2-15=201

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