Solve for a a^2b-c=d

$a^{2} b - c = d$

Add $c$ to both sides of the equation.

$a^{2} b = d + c$

Divide each term in $a^{2} b = d + c$ by $b$ and simplify.

Divide each term in $a^{2} b = d + c$ by $b$ .

$\frac{a^{2} b}{b} = \frac{d}{b} + \frac{c}{b}$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{a^{2} b}{b} = \frac{d}{b} + \frac{c}{b}$

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

$a^{2} = \frac{d}{b} + \frac{c}{b}$

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

$a = \pm \sqrt{\frac{d}{b} + \frac{c}{b}}$

Simplify $\pm \sqrt{\frac{d}{b} + \frac{c}{b}}$ .

Combine the numerators over the common denominator.

$a = \pm \sqrt{\frac{d + c}{b}}$

Rewrite $\sqrt{\frac{d + c}{b}}$ as $\frac{\sqrt{d + c}}{\sqrt{b}}$ .

$a = \pm \frac{\sqrt{d + c}}{\sqrt{b}}$

Multiply $\frac{\sqrt{d + c}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$a = \pm \frac{\sqrt{d + c}}{\sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{d + c}}{\sqrt{b}}$ by $\frac{\sqrt{b}}{\sqrt{b}}$ .

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{\sqrt{b} \sqrt{b}}$

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{{\sqrt{b}}^{1} \sqrt{b}}$

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{{\sqrt{b}}^{1} {\sqrt{b}}^{1}}$

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{{\sqrt{b}}^{1 + 1}}$

Add $1$ and $1$ .

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{{\sqrt{b}}^{2}}$

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

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{{(b^{\frac{1}{2}})}^{2}}$

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{b^{\frac{1}{2} \cdot 2}}$

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

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{b^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{b^{\frac{2}{2}}}$

Rewrite the expression.

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{b^{1}}$

Simplify.

$a = \pm \frac{\sqrt{d + c} \sqrt{b}}{b}$

Combine using the product rule for radicals.

$a = \pm \frac{\sqrt{(d + c) b}}{b}$

Reorder factors in $\pm \frac{\sqrt{(d + c) b}}{b}$ .

$a = \pm \frac{\sqrt{b (d + c)}}{b}$

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.

$a = \frac{\sqrt{b (d + c)}}{b}$

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

$a = - \frac{\sqrt{b (d + c)}}{b}$

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

$a = \frac{\sqrt{b (d + c)}}{b}$

$a = - \frac{\sqrt{b (d + c)}}{b}$

$a = \frac{\sqrt{b (d + c)}}{b}$

$a = - \frac{\sqrt{b (d + c)}}{b}$

Solve for a a^2b-c=d

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