Solve for z square root of 5z-11 = square root of 2z+10

$\sqrt{5 z - 11} = \sqrt{2 z + 10}$

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

${\sqrt{5 z - 11}}^{2} = {\sqrt{2 z + 10}}^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(5 z - 11)}^{\frac{1}{2}})}^{2}$ .

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

${(5 z - 11)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 z + 10}}^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(5 z - 11)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 z + 10}}^{2}$

Rewrite the expression.

${(5 z - 11)}^{1} = {\sqrt{2 z + 10}}^{2}$

Simplify.

$5 z - 11 = {\sqrt{2 z + 10}}^{2}$

Factor $2$ out of $2 z + 10$ .

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Factor $2$ out of $2 z$ .

$5 z - 11 = {\sqrt{2 (z) + 10}}^{2}$

Factor $2$ out of $10$ .

$5 z - 11 = {\sqrt{2 z + 2 \cdot 5}}^{2}$

Factor $2$ out of $2 z + 2 \cdot 5$ .

$5 z - 11 = {\sqrt{2 (z + 5)}}^{2}$

Rewrite ${\sqrt{2 (z + 5)}}^{2}$ as $2 (z + 5)$ .

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

$5 z - 11 = {({(2 (z + 5))}^{\frac{1}{2}})}^{2}$

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

$5 z - 11 = {(2 (z + 5))}^{\frac{1}{2} \cdot 2}$

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

$5 z - 11 = {(2 (z + 5))}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$5 z - 11 = {(2 (z + 5))}^{\frac{2}{2}}$

Divide $1$ by $1$ .

$5 z - 11 = {(2 (z + 5))}^{1}$

Simplify.

$5 z - 11 = 2 (z + 5)$

Apply the distributive property.

$5 z - 11 = 2 z + 2 \cdot 5$

Multiply $2$ by $5$ .

$5 z - 11 = 2 z + 10$

Solve for $z$ .

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Move all terms containing $z$ to the left side of the equation.

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Subtract $2 z$ from both sides of the equation.

$5 z - 11 - 2 z = 10$

Subtract $2 z$ from $5 z$ .

$3 z - 11 = 10$

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

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Add $11$ to both sides of the equation.

$3 z = 10 + 11$

Add $10$ and $11$ .

$3 z = 21$

Divide each term by $3$ and simplify.

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Divide each term in $3 z = 21$ by $3$ .

$\frac{3 z}{3} = \frac{21}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 z}{3} = \frac{21}{3}$

Divide $z$ by $1$ .

$z = \frac{21}{3}$

Divide $21$ by $3$ .

$z = 7$

Solve for z square root of 5z-11 = square root of 2z+10

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