Solve the Rational Equation for x square root of 5x-10+9=4

$\sqrt{5 x - 10} + 9 = 4$

Move all terms not containing $\sqrt{5 x - 10}$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$\sqrt{5 x - 10} = 4 - 9$

Subtract $9$ from $4$ .

$\sqrt{5 x - 10} = - 5$

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

${\sqrt{5 x - 10}}^{2} = {(- 5)}^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 10}$ as ${(5 x - 10)}^{\frac{1}{2}}$ .

${({(5 x - 10)}^{\frac{1}{2}})}^{2} = {(- 5)}^{2}$

Simplify the left side.

Simplify ${({(5 x - 10)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x - 10)}^{\frac{1}{2}})}^{2}$ .

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

${(5 x - 10)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x - 10)}^{\frac{1}{2} \cdot 2} = {(- 5)}^{2}$

Rewrite the expression.

${(5 x - 10)}^{1} = {(- 5)}^{2}$

Simplify.

$5 x - 10 = {(- 5)}^{2}$

Simplify the right side.

Raise $- 5$ to the power of $2$ .

$5 x - 10 = 25$

Solve for $x$ .

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

Add $10$ to both sides of the equation.

$5 x = 25 + 10$

Add $25$ and $10$ .

$5 x = 35$

Divide each term in $5 x = 35$ by $5$ and simplify.

Divide each term in $5 x = 35$ by $5$ .

$\frac{5 x}{5} = \frac{35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{35}{5}$

Divide $x$ by $1$ .

$x = \frac{35}{5}$

Simplify the right side.

Divide $35$ by $5$ .

$x = 7$

Exclude the solutions that do not make $\sqrt{5 x - 10} + 9 = 4$ true.

$No solution$

Solve the Rational Equation for x square root of 5x-10+9=4

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