Solve for j 8 square root of 9j+10=1

$8 \sqrt{9 j} + 10 = 1$

Step 1

Move all terms not containing $8 \sqrt{9 j}$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$8 \sqrt{9 j} = 1 - 10$

Subtract $10$ from $1$ .

$8 \sqrt{9 j} = - 9$

Step 2

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

${(8 \sqrt{9 j})}^{2} = {(- 9)}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 j}$ as ${(9 j)}^{\frac{1}{2}}$ .

${(8 {(9 j)}^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Simplify the left side.

Simplify ${(8 {(9 j)}^{\frac{1}{2}})}^{2}$ .

Simplify the expression.

Apply the product rule to $9 j$ .

${(8 (9^{\frac{1}{2}} j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

Rewrite $9$ as $3^{2}$ .

${(8 ({(3^{2})}^{\frac{1}{2}} j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

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

${(8 (3^{2 (\frac{1}{2})} j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 (3^{2 (\frac{1}{2})} j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

Rewrite the expression.

${(8 (3^{1} j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

Evaluate the exponent.

${(8 (3 j^{\frac{1}{2}}))}^{2} = {(- 9)}^{2}$

Multiply $3$ by $8$ .

${(24 j^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Apply the product rule to $24 j^{\frac{1}{2}}$ .

$24^{2} {(j^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Raise $24$ to the power of $2$ .

$576 {(j^{\frac{1}{2}})}^{2} = {(- 9)}^{2}$

Multiply the exponents in ${(j^{\frac{1}{2}})}^{2}$ .

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

$576 j^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$576 j^{\frac{1}{2} \cdot 2} = {(- 9)}^{2}$

Rewrite the expression.

$576 j^{1} = {(- 9)}^{2}$

Simplify.

$576 j = {(- 9)}^{2}$

Simplify the right side.

Raise $- 9$ to the power of $2$ .

$576 j = 81$

Step 4

Divide each term in $576 j = 81$ by $576$ and simplify.

Divide each term in $576 j = 81$ by $576$ .

$\frac{576 j}{576} = \frac{81}{576}$

Simplify the left side.

Cancel the common factor of $576$ .

Cancel the common factor.

$\frac{576 j}{576} = \frac{81}{576}$

Divide $j$ by $1$ .

$j = \frac{81}{576}$

Simplify the right side.

Cancel the common factor of $81$ and $576$ .

Factor $9$ out of $81$ .

$j = \frac{9 (9)}{576}$

Cancel the common factors.

Factor $9$ out of $576$ .

$j = \frac{9 \cdot 9}{9 \cdot 64}$

Cancel the common factor.

$j = \frac{9 \cdot 9}{9 \cdot 64}$

Rewrite the expression.

$j = \frac{9}{64}$

Step 5

Exclude the solutions that do not make $8 \sqrt{9 j} + 10 = 1$ true.

$No solution$

Solve for j 8 square root of 9j+10=1

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