Evaluate square root of 5x-1+4=1

$\sqrt{5 x - 1} + 4 = 1$

Step 1

Move all terms not containing $\sqrt{5 x - 1}$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$\sqrt{5 x - 1} = 1 - 4$

Subtract $4$ from $1$ .

$\sqrt{5 x - 1} = - 3$

Step 2

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

${\sqrt{5 x - 1}}^{2} = {(- 3)}^{2}$

Step 3

Simplify each side of the equation.

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

${({(5 x - 1)}^{\frac{1}{2}})}^{2} = {(- 3)}^{2}$

Simplify the left side.

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

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

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

${(5 x - 1)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x - 1)}^{\frac{1}{2} \cdot 2} = {(- 3)}^{2}$

Rewrite the expression.

${(5 x - 1)}^{1} = {(- 3)}^{2}$

Simplify.

$5 x - 1 = {(- 3)}^{2}$

Simplify the right side.

Raise $- 3$ to the power of $2$ .

$5 x - 1 = 9$

Step 4

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$5 x = 9 + 1$

Add $9$ and $1$ .

$5 x = 10$

Divide each term in $5 x = 10$ by $5$ and simplify.

Divide each term in $5 x = 10$ by $5$ .

$\frac{5 x}{5} = \frac{10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{10}{5}$

Divide $x$ by $1$ .

$x = \frac{10}{5}$

Simplify the right side.

Divide $10$ by $5$ .

$x = 2$

Step 5

Exclude the solutions that do not make $\sqrt{5 x - 1} + 4 = 1$ true.

$No solution$

Evaluate square root of 5x-1+4=1

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