Solve the Rational Equation for x 5 square root of 5x+2=10

$5 \sqrt{5 x + 2} = 10$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

Apply the product rule to $5 {(5 x + 2)}^{\frac{1}{2}}$ .

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

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

$25 {({(5 x + 2)}^{\frac{1}{2}})}^{2} = 10^{2}$

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

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

$25 {(5 x + 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 {(5 x + 2)}^{\frac{1}{2} \cdot 2} = 10^{2}$

Rewrite the expression.

$25 {(5 x + 2)}^{1} = 10^{2}$

Simplify.

$25 (5 x + 2) = 10^{2}$

Apply the distributive property.

$25 (5 x) + 25 \cdot 2 = 10^{2}$

Multiply.

Multiply $5$ by $25$ .

$125 x + 25 \cdot 2 = 10^{2}$

Multiply $25$ by $2$ .

$125 x + 50 = 10^{2}$

Simplify the right side.

Raise $10$ to the power of $2$ .

$125 x + 50 = 100$

Solve for $x$ .

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

Subtract $50$ from both sides of the equation.

$125 x = 100 - 50$

Subtract $50$ from $100$ .

$125 x = 50$

Divide each term in $125 x = 50$ by $125$ and simplify.

Divide each term in $125 x = 50$ by $125$ .

$\frac{125 x}{125} = \frac{50}{125}$

Simplify the left side.

Cancel the common factor of $125$ .

Cancel the common factor.

$\frac{125 x}{125} = \frac{50}{125}$

Divide $x$ by $1$ .

$x = \frac{50}{125}$

Simplify the right side.

Cancel the common factor of $50$ and $125$ .

Factor $25$ out of $50$ .

$x = \frac{25 (2)}{125}$

Cancel the common factors.

Factor $25$ out of $125$ .

$x = \frac{25 \cdot 2}{25 \cdot 5}$

Cancel the common factor.

$x = \frac{25 \cdot 2}{25 \cdot 5}$

Rewrite the expression.

$x = \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{5}$

Decimal Form:

$x = 0.4$

Solve the Rational Equation for x 5 square root of 5x+2=10

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