Algebra Examples

$\sqrt{2 d - 1} = 5$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 d - 1}}^{2} = 5^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${({(2 d - 1)}^{\frac{1}{2}})}^{2} = 5^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(2 d - 1)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(2 d - 1)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1.1

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

${(2 d - 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(2 d - 1)}^{\frac{1}{2} \cdot 2} = 5^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 d - 1)}^{1} = 5^{2}$

Step 2.2.1.2

Simplify.

$2 d - 1 = 5^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $5$ to the power of $2$ .

$2 d - 1 = 25$

Step 3

Solve for $d$ .

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Step 3.1

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

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Step 3.1.1

Add $1$ to both sides of the equation.

$2 d = 25 + 1$

Step 3.1.2

Add $25$ and $1$ .

$2 d = 26$

Step 3.2

Divide each term in $2 d = 26$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 d = 26$ by $2$ .

$\frac{2 d}{2} = \frac{26}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 d}{2} = \frac{26}{2}$

Step 3.2.2.1.2

Divide $d$ by $1$ .

$d = \frac{26}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $26$ by $2$ .

$d = 13$