Solve for y 5+ square root of 4y-5=12

$5 + \sqrt{4 y - 5} = 12$

Step 1

Move all terms not containing $\sqrt{4 y - 5}$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$\sqrt{4 y - 5} = 12 - 5$

Subtract $5$ from $12$ .

$\sqrt{4 y - 5} = 7$

Step 2

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

${\sqrt{4 y - 5}}^{2} = 7^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 y - 5}$ as ${(4 y - 5)}^{\frac{1}{2}}$ .

${({(4 y - 5)}^{\frac{1}{2}})}^{2} = 7^{2}$

Simplify the left side.

Simplify ${({(4 y - 5)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(4 y - 5)}^{\frac{1}{2}})}^{2}$ .

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

${(4 y - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(4 y - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Rewrite the expression.

${(4 y - 5)}^{1} = 7^{2}$

Simplify.

$4 y - 5 = 7^{2}$

Simplify the right side.

Raise $7$ to the power of $2$ .

$4 y - 5 = 49$

Step 4

Solve for $y$ .

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

Add $5$ to both sides of the equation.

$4 y = 49 + 5$

Add $49$ and $5$ .

$4 y = 54$

Divide each term in $4 y = 54$ by $4$ and simplify.

Divide each term in $4 y = 54$ by $4$ .

$\frac{4 y}{4} = \frac{54}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{54}{4}$

Divide $y$ by $1$ .

$y = \frac{54}{4}$

Simplify the right side.

Cancel the common factor of $54$ and $4$ .

Factor $2$ out of $54$ .

$y = \frac{2 (27)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 27}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot 27}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{27}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{27}{2}$

Decimal Form:

$y = 13.5$

Mixed Number Form:

$y = 13 \frac{1}{2}$

Solve for y 5+ square root of 4y-5=12

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