Solve Using the Quadratic Formula x^2=3/8x

$x^{2} = \frac{3}{8} x$

Step 1

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

Simplify the right side.

Combine $\frac{3}{8}$ and $x$ .

$x^{2} = \frac{3 x}{8}$

Subtract $\frac{3 x}{8}$ from both sides of the equation.

$x^{2} - \frac{3 x}{8} = 0$

Step 2

Multiply through by the least common denominator $8$ , then simplify.

Apply the distributive property.

$8 x^{2} + 8 (- \frac{3 x}{8}) = 0$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{3 x}{8}$ into the numerator.

$8 x^{2} + 8 (\frac{- 3 x}{8}) = 0$

Cancel the common factor.

$8 x^{2} + 8 (\frac{- 3 x}{8}) = 0$

Rewrite the expression.

$8 x^{2} - 3 x = 0$

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 $a = 8$ , $b = - 3$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (8 \cdot 0)}}{2 \cdot 8}$

Step 5

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 8 \cdot 0}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot 0$ .

Multiply $- 4$ by $8$ .

$x = \frac{3 \pm \sqrt{9 - 32 \cdot 0}}{2 \cdot 8}$

Multiply $- 32$ by $0$ .

$x = \frac{3 \pm \sqrt{9 + 0}}{2 \cdot 8}$

Add $9$ and $0$ .

$x = \frac{3 \pm \sqrt{9}}{2 \cdot 8}$

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

$x = \frac{3 \pm \sqrt{3^{2}}}{2 \cdot 8}$

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

$x = \frac{3 \pm 3}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{3 \pm 3}{16}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{3}{8}, 0$

Solve Using the Quadratic Formula x^2=3/8x

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