Solve for p square root of 6-5p = square root of 3p-26

$\sqrt{6 - 5 p} = \sqrt{3 p - 26}$

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

${\sqrt{6 - 5 p}}^{2} = {\sqrt{3 p - 26}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 - 5 p}$ as ${(6 - 5 p)}^{\frac{1}{2}}$ .

${({(6 - 5 p)}^{\frac{1}{2}})}^{2} = {\sqrt{3 p - 26}}^{2}$

Simplify the left side.

Simplify ${({(6 - 5 p)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(6 - 5 p)}^{\frac{1}{2}})}^{2}$ .

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

${(6 - 5 p)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 p - 26}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(6 - 5 p)}^{\frac{1}{2} \cdot 2} = {\sqrt{3 p - 26}}^{2}$

Rewrite the expression.

${(6 - 5 p)}^{1} = {\sqrt{3 p - 26}}^{2}$

Simplify.

$6 - 5 p = {\sqrt{3 p - 26}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{3 p - 26}}^{2}$ as $3 p - 26$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 p - 26}$ as ${(3 p - 26)}^{\frac{1}{2}}$ .

$6 - 5 p = {({(3 p - 26)}^{\frac{1}{2}})}^{2}$

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

$6 - 5 p = {(3 p - 26)}^{\frac{1}{2} \cdot 2}$

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

$6 - 5 p = {(3 p - 26)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6 - 5 p = {(3 p - 26)}^{\frac{2}{2}}$

Rewrite the expression.

$6 - 5 p = {(3 p - 26)}^{1}$

Simplify.

$6 - 5 p = 3 p - 26$

Solve for $p$ .

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

Subtract $3 p$ from both sides of the equation.

$6 - 5 p - 3 p = - 26$

Subtract $3 p$ from $- 5 p$ .

$6 - 8 p = - 26$

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

Subtract $6$ from both sides of the equation.

$- 8 p = - 26 - 6$

Subtract $6$ from $- 26$ .

$- 8 p = - 32$

Divide each term in $- 8 p = - 32$ by $- 8$ and simplify.

Divide each term in $- 8 p = - 32$ by $- 8$ .

$\frac{- 8 p}{- 8} = \frac{- 32}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 p}{- 8} = \frac{- 32}{- 8}$

Divide $p$ by $1$ .

$p = \frac{- 32}{- 8}$

Simplify the right side.

Divide $- 32$ by $- 8$ .

$p = 4$

Exclude the solutions that do not make $\sqrt{6 - 5 p} = \sqrt{3 p - 26}$ true.

$No solution$

Solve for p square root of 6-5p = square root of 3p-26

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