Solve the Rational Equation for x -5 square root of x-1=20

$- 5 \sqrt{x - 1} = 20$

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

${(- 5 \sqrt{x - 1})}^{2} = 20^{2}$

Simplify each side of the equation.

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

${(- 5 {(x - 1)}^{\frac{1}{2}})}^{2} = 20^{2}$

Simplify the left side.

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

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

${(- 5)}^{2} {({(x - 1)}^{\frac{1}{2}})}^{2} = 20^{2}$

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

$25 {({(x - 1)}^{\frac{1}{2}})}^{2} = 20^{2}$

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

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

$25 {(x - 1)}^{\frac{1}{2} \cdot 2} = 20^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 {(x - 1)}^{\frac{1}{2} \cdot 2} = 20^{2}$

Rewrite the expression.

$25 {(x - 1)}^{1} = 20^{2}$

Simplify.

$25 (x - 1) = 20^{2}$

Apply the distributive property.

$25 x + 25 \cdot - 1 = 20^{2}$

Multiply $25$ by $- 1$ .

$25 x - 25 = 20^{2}$

Simplify the right side.

Raise $20$ to the power of $2$ .

$25 x - 25 = 400$

Solve for $x$ .

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

Add $25$ to both sides of the equation.

$25 x = 400 + 25$

Add $400$ and $25$ .

$25 x = 425$

Divide each term in $25 x = 425$ by $25$ and simplify.

Divide each term in $25 x = 425$ by $25$ .

$\frac{25 x}{25} = \frac{425}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} = \frac{425}{25}$

Divide $x$ by $1$ .

$x = \frac{425}{25}$

Simplify the right side.

Divide $425$ by $25$ .

$x = 17$

Exclude the solutions that do not make $- 5 \sqrt{x - 1} = 20$ true.

$No solution$

Solve the Rational Equation for x -5 square root of x-1=20

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