Solve Using the Quadratic Formula x^2=-6/7x

$x^{2} = - \frac{6}{7} x$

Step 1

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

Simplify the right side.

Simplify $- \frac{6}{7} x$ .

Combine $x$ and $\frac{6}{7}$ .

$x^{2} = - \frac{x \cdot 6}{7}$

Move $6$ to the left of $x$ .

$x^{2} = - \frac{6 x}{7}$

Add $\frac{6 x}{7}$ to both sides of the equation.

$x^{2} + \frac{6 x}{7} = 0$

Step 2

Multiply through by the least common denominator $7$ , then simplify.

Apply the distributive property.

$7 x^{2} + 7 (\frac{6 x}{7}) = 0$

Cancel the common factor of $7$ .

Cancel the common factor.

$7 x^{2} + 7 (\frac{6 x}{7}) = 0$

Rewrite the expression.

$7 x^{2} + 6 x = 0$

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 $a = 7$ , $b = 6$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (7 \cdot 0)}}{2 \cdot 7}$

Step 5

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 7 \cdot 0}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot 0$ .

Multiply $- 4$ by $7$ .

$x = \frac{- 6 \pm \sqrt{36 - 28 \cdot 0}}{2 \cdot 7}$

Multiply $- 28$ by $0$ .

$x = \frac{- 6 \pm \sqrt{36 + 0}}{2 \cdot 7}$

Add $36$ and $0$ .

$x = \frac{- 6 \pm \sqrt{36}}{2 \cdot 7}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 6 \pm \sqrt{6^{2}}}{2 \cdot 7}$

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

$x = \frac{- 6 \pm 6}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{- 6 \pm 6}{14}$

Simplify $\frac{- 6 \pm 6}{14}$ .

$x = \frac{- 3 \pm 3}{7}$

Step 6

The final answer is the combination of both solutions.

$x = 0, - \frac{6}{7}$

Solve Using the Quadratic Formula x^2=-6/7x

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