Solve Using the Quadratic Formula x^2=-7/9x

$x^{2} = - \frac{7}{9} x$

Step 1

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

Simplify the right side.

Simplify $- \frac{7}{9} x$ .

Combine $x$ and $\frac{7}{9}$ .

$x^{2} = - \frac{x \cdot 7}{9}$

Move $7$ to the left of $x$ .

$x^{2} = - \frac{7 x}{9}$

Add $\frac{7 x}{9}$ to both sides of the equation.

$x^{2} + \frac{7 x}{9} = 0$

Step 2

Multiply through by the least common denominator $9$ , then simplify.

Apply the distributive property.

$9 x^{2} + 9 (\frac{7 x}{9}) = 0$

Cancel the common factor of $9$ .

Cancel the common factor.

$9 x^{2} + 9 (\frac{7 x}{9}) = 0$

Rewrite the expression.

$9 x^{2} + 7 x = 0$

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 $a = 9$ , $b = 7$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (9 \cdot 0)}}{2 \cdot 9}$

Step 5

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 9 \cdot 0}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot 0$ .

Multiply $- 4$ by $9$ .

$x = \frac{- 7 \pm \sqrt{49 - 36 \cdot 0}}{2 \cdot 9}$

Multiply $- 36$ by $0$ .

$x = \frac{- 7 \pm \sqrt{49 + 0}}{2 \cdot 9}$

Add $49$ and $0$ .

$x = \frac{- 7 \pm \sqrt{49}}{2 \cdot 9}$

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

$x = \frac{- 7 \pm \sqrt{7^{2}}}{2 \cdot 9}$

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

$x = \frac{- 7 \pm 7}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{- 7 \pm 7}{18}$

Step 6

The final answer is the combination of both solutions.

$x = 0, - \frac{7}{9}$

Solve Using the Quadratic Formula x^2=-7/9x

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