Algebra Examples

$6 - \sqrt{y - 5} = 3$

Step 1

Move all terms not containing $- \sqrt{y - 5}$ to the right side of the equation.

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Step 1.1

Subtract $6$ from both sides of the equation.

$- \sqrt{y - 5} = 3 - 6$

Step 1.2

Subtract $6$ from $3$ .

$- \sqrt{y - 5} = - 3$

Step 2

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

${(- \sqrt{y - 5})}^{2} = {(- 3)}^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y - 5}$ as ${(y - 5)}^{\frac{1}{2}}$ .

${(- {(y - 5)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- {(y - 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $- {(y - 5)}^{\frac{1}{2}}$ .

${(- 1)}^{2} {({(y - 5)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Step 3.2.1.2

Raise $- 1$ to the power of $2$ .

$1 {({(y - 5)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Step 3.2.1.3

Multiply ${({(y - 5)}^{\frac{1}{2}})}^{2}$ by $1$ .

${({(y - 5)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Step 3.2.1.4

Multiply the exponents in ${({(y - 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.4.1

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

${(y - 5)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Step 3.2.1.4.2

Cancel the common factor of $2$ .

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Step 3.2.1.4.2.1

Cancel the common factor.

${(y - 5)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Step 3.2.1.4.2.2

Rewrite the expression.

${(y - 5)}^{1} = {(- 3)}^{2}$

Step 3.2.1.5

Simplify.

$y - 5 = {(- 3)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$y - 5 = 9$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$y = 9 + 5$

Step 4.2

Add $9$ and $5$ .

$y = 14$