Solve for x A=P(1+x/100)^2

$A = P {(1 + \frac{x}{100})}^{2}$

Step 1

Rewrite the equation as $P {(1 + \frac{x}{100})}^{2} = A$ .

$P {(1 + \frac{x}{100})}^{2} = A$

Step 2

Divide each term in $P {(1 + \frac{x}{100})}^{2} = A$ by $P$ and simplify.

Divide each term in $P {(1 + \frac{x}{100})}^{2} = A$ by $P$ .

$\frac{P {(1 + \frac{x}{100})}^{2}}{P} = \frac{A}{P}$

Simplify the left side.

Cancel the common factor of $P$ .

Cancel the common factor.

$\frac{P {(1 + \frac{x}{100})}^{2}}{P} = \frac{A}{P}$

Divide ${(1 + \frac{x}{100})}^{2}$ by $1$ .

${(1 + \frac{x}{100})}^{2} = \frac{A}{P}$

Step 3

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

$1 + \frac{x}{100} = \pm \sqrt{\frac{A}{P}}$

Step 4

Simplify $\pm \sqrt{\frac{A}{P}}$ .

Rewrite $\sqrt{\frac{A}{P}}$ as $\frac{\sqrt{A}}{\sqrt{P}}$ .

$1 + \frac{x}{100} = \pm \frac{\sqrt{A}}{\sqrt{P}}$

Multiply $\frac{\sqrt{A}}{\sqrt{P}}$ by $\frac{\sqrt{P}}{\sqrt{P}}$ .

$1 + \frac{x}{100} = \pm \frac{\sqrt{A}}{\sqrt{P}} \cdot \frac{\sqrt{P}}{\sqrt{P}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt{A}}{\sqrt{P}}$ by $\frac{\sqrt{P}}{\sqrt{P}}$ .

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{\sqrt{P} \sqrt{P}}$

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{{\sqrt{P}}^{1} \sqrt{P}}$

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{{\sqrt{P}}^{1} {\sqrt{P}}^{1}}$

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{{\sqrt{P}}^{1 + 1}}$

Add $1$ and $1$ .

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{{\sqrt{P}}^{2}}$

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

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{{(P^{\frac{1}{2}})}^{2}}$

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{P^{\frac{1}{2} \cdot 2}}$

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

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{P^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{P^{\frac{2}{2}}}$

Rewrite the expression.

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{P^{1}}$

Simplify.

$1 + \frac{x}{100} = \pm \frac{\sqrt{A} \sqrt{P}}{P}$

Combine using the product rule for radicals.

$1 + \frac{x}{100} = \pm \frac{\sqrt{A P}}{P}$

Step 5

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.

$1 + \frac{x}{100} = \frac{\sqrt{A P}}{P}$

Subtract $1$ from both sides of the equation.

$\frac{x}{100} = \frac{\sqrt{A P}}{P} - 1$

Multiply both sides of the equation by $100$ .

$100 \frac{x}{100} = 100 (\frac{\sqrt{A P}}{P} - 1)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$100 \frac{x}{100} = 100 (\frac{\sqrt{A P}}{P} - 1)$

Rewrite the expression.

$x = 100 (\frac{\sqrt{A P}}{P} - 1)$

Simplify the right side.

Simplify $100 (\frac{\sqrt{A P}}{P} - 1)$ .

Apply the distributive property.

$x = 100 \frac{\sqrt{A P}}{P} + 100 \cdot - 1$

Combine $100$ and $\frac{\sqrt{A P}}{P}$ .

$x = \frac{100 \sqrt{A P}}{P} + 100 \cdot - 1$

Multiply $100$ by $- 1$ .

$x = \frac{100 \sqrt{A P}}{P} - 100$

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

$1 + \frac{x}{100} = - \frac{\sqrt{A P}}{P}$

Subtract $1$ from both sides of the equation.

$\frac{x}{100} = - \frac{\sqrt{A P}}{P} - 1$

Multiply both sides of the equation by $100$ .

$100 \frac{x}{100} = 100 (- \frac{\sqrt{A P}}{P} - 1)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $100$ .

Cancel the common factor.

$100 \frac{x}{100} = 100 (- \frac{\sqrt{A P}}{P} - 1)$

Rewrite the expression.

$x = 100 (- \frac{\sqrt{A P}}{P} - 1)$

Simplify the right side.

Simplify $100 (- \frac{\sqrt{A P}}{P} - 1)$ .

Apply the distributive property.

$x = 100 (- \frac{\sqrt{A P}}{P}) + 100 \cdot - 1$

Multiply $100 (- \frac{\sqrt{A P}}{P})$ .

Multiply $- 1$ by $100$ .

$x = - 100 \frac{\sqrt{A P}}{P} + 100 \cdot - 1$

Combine $- 100$ and $\frac{\sqrt{A P}}{P}$ .

$x = \frac{- 100 \sqrt{A P}}{P} + 100 \cdot - 1$

Multiply $100$ by $- 1$ .

$x = \frac{- 100 \sqrt{A P}}{P} - 100$

Move the negative in front of the fraction.

$x = - \frac{100 \sqrt{A P}}{P} - 100$

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

$x = \frac{100 \sqrt{A P}}{P} - 100$

$x = - \frac{100 \sqrt{A P}}{P} - 100$

$x = \frac{100 \sqrt{A P}}{P} - 100$

$x = - \frac{100 \sqrt{A P}}{P} - 100$

Solve for x A=P(1+x/100)^2

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