Solve for d square root of 7d+2 = square root of 10d-1

$\sqrt{7 d + 2} = \sqrt{10 d - 1}$

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

${\sqrt{7 d + 2}}^{2} = {\sqrt{10 d - 1}}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 d + 2}$ as ${(7 d + 2)}^{\frac{1}{2}}$ .

${({(7 d + 2)}^{\frac{1}{2}})}^{2} = {\sqrt{10 d - 1}}^{2}$

Simplify the left side.

Simplify ${({(7 d + 2)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 d + 2)}^{\frac{1}{2}})}^{2}$ .

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

${(7 d + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{10 d - 1}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 d + 2)}^{\frac{1}{2} \cdot 2} = {\sqrt{10 d - 1}}^{2}$

Rewrite the expression.

${(7 d + 2)}^{1} = {\sqrt{10 d - 1}}^{2}$

Simplify.

$7 d + 2 = {\sqrt{10 d - 1}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{10 d - 1}}^{2}$ as $10 d - 1$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10 d - 1}$ as ${(10 d - 1)}^{\frac{1}{2}}$ .

$7 d + 2 = {({(10 d - 1)}^{\frac{1}{2}})}^{2}$

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

$7 d + 2 = {(10 d - 1)}^{\frac{1}{2} \cdot 2}$

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

$7 d + 2 = {(10 d - 1)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 d + 2 = {(10 d - 1)}^{\frac{2}{2}}$

Rewrite the expression.

$7 d + 2 = {(10 d - 1)}^{1}$

Simplify.

$7 d + 2 = 10 d - 1$

Solve for $d$ .

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

Subtract $10 d$ from both sides of the equation.

$7 d + 2 - 10 d = - 1$

Subtract $10 d$ from $7 d$ .

$- 3 d + 2 = - 1$

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

Subtract $2$ from both sides of the equation.

$- 3 d = - 1 - 2$

Subtract $2$ from $- 1$ .

$- 3 d = - 3$

Divide each term in $- 3 d = - 3$ by $- 3$ and simplify.

Divide each term in $- 3 d = - 3$ by $- 3$ .

$\frac{- 3 d}{- 3} = \frac{- 3}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 d}{- 3} = \frac{- 3}{- 3}$

Divide $d$ by $1$ .

$d = \frac{- 3}{- 3}$

Simplify the right side.

Divide $- 3$ by $- 3$ .

$d = 1$

Solve for d square root of 7d+2 = square root of 10d-1

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