Solve for x a=(dx^2)/v

$a = \frac{d x^{2}}{v}$

Step 1

Rewrite the equation as $\frac{d x^{2}}{v} = a$ .

$\frac{d x^{2}}{v} = a$

Step 2

Multiply both sides by $v$ .

$\frac{d x^{2}}{v} v = a v$

Step 3

Simplify the left side.

Cancel the common factor of $v$ .

Cancel the common factor.

$\frac{d x^{2}}{v} v = a v$

Rewrite the expression.

$d x^{2} = a v$

Step 4

Solve for $x$ .

Divide each term in $d x^{2} = a v$ by $d$ and simplify.

Divide each term in $d x^{2} = a v$ by $d$ .

$\frac{d x^{2}}{d} = \frac{a v}{d}$

Simplify the left side.

Cancel the common factor of $d$ .

Cancel the common factor.

$\frac{d x^{2}}{d} = \frac{a v}{d}$

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

$x^{2} = \frac{a v}{d}$

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

$x = \pm \sqrt{\frac{a v}{d}}$

Simplify $\pm \sqrt{\frac{a v}{d}}$ .

Rewrite $\sqrt{\frac{a v}{d}}$ as $\frac{\sqrt{a v}}{\sqrt{d}}$ .

$x = \pm \frac{\sqrt{a v}}{\sqrt{d}}$

Multiply $\frac{\sqrt{a v}}{\sqrt{d}}$ by $\frac{\sqrt{d}}{\sqrt{d}}$ .

$x = \pm \frac{\sqrt{a v}}{\sqrt{d}} \cdot \frac{\sqrt{d}}{\sqrt{d}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{a v}}{\sqrt{d}}$ by $\frac{\sqrt{d}}{\sqrt{d}}$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{\sqrt{d} \sqrt{d}}$

Raise $\sqrt{d}$ to the power of $1$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{{\sqrt{d}}^{1} \sqrt{d}}$

Raise $\sqrt{d}$ to the power of $1$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{{\sqrt{d}}^{1} {\sqrt{d}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{{\sqrt{d}}^{1 + 1}}$

Add $1$ and $1$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{{\sqrt{d}}^{2}}$

Rewrite ${\sqrt{d}}^{2}$ as $d$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{d}$ as $d^{\frac{1}{2}}$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{{(d^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{d^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{d^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{d^{\frac{2}{2}}}$

Rewrite the expression.

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{d^{1}}$

Simplify.

$x = \pm \frac{\sqrt{a v} \sqrt{d}}{d}$

Combine using the product rule for radicals.

$x = \pm \frac{\sqrt{a v d}}{d}$

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.

$x = \frac{\sqrt{a v d}}{d}$

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

$x = - \frac{\sqrt{a v d}}{d}$

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

$x = \frac{\sqrt{a v d}}{d}$

$x = - \frac{\sqrt{a v d}}{d}$

$x = \frac{\sqrt{a v d}}{d}$

$x = - \frac{\sqrt{a v d}}{d}$

$x = \frac{\sqrt{a v d}}{d}$

$x = - \frac{\sqrt{a v d}}{d}$

Solve for x a=(dx^2)/v

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