Basic Math Examples

${(3 \sqrt{14})}^{2} = 125 + y^{2}$

Step 1

Rewrite the equation as $125 + y^{2} = {(3 \sqrt{14})}^{2}$ .

$125 + y^{2} = {(3 \sqrt{14})}^{2}$

Step 2

Simplify ${(3 \sqrt{14})}^{2}$ .

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Step 2.1

Rewrite.

$125 + y^{2} = 0 + 0 + {(3 \sqrt{14})}^{2}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Apply the product rule to $3 \sqrt{14}$ .

$125 + y^{2} = 3^{2} {\sqrt{14}}^{2}$

Step 2.2.2

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

$125 + y^{2} = 9 {\sqrt{14}}^{2}$

Step 2.3

Rewrite ${\sqrt{14}}^{2}$ as $14$ .

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Step 2.3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14}$ as $14^{\frac{1}{2}}$ .

$125 + y^{2} = 9 {(14^{\frac{1}{2}})}^{2}$

Step 2.3.2

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

$125 + y^{2} = 9 \cdot 14^{\frac{1}{2} \cdot 2}$

Step 2.3.3

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

$125 + y^{2} = 9 \cdot 14^{\frac{2}{2}}$

Step 2.3.4

Cancel the common factor of $2$ .

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Step 2.3.4.1

Cancel the common factor.

$125 + y^{2} = 9 \cdot 14^{\frac{2}{2}}$

Step 2.3.4.2

Rewrite the expression.

$125 + y^{2} = 9 \cdot 14^{1}$

Step 2.3.5

Evaluate the exponent.

$125 + y^{2} = 9 \cdot 14$

Step 2.4

Multiply $9$ by $14$ .

$125 + y^{2} = 126$

Step 3

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1

Subtract $125$ from both sides of the equation.

$y^{2} = 126 - 125$

Step 3.2

Subtract $125$ from $126$ .

$y^{2} = 1$

Step 4

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

$y = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$y = \pm 1$

Step 6

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

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Step 6.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 1$

Step 6.2

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

$y = - 1$

Step 6.3

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

$y = 1, - 1$