Solve for x 2 square root of x-1+3=1

$2 \sqrt{x - 1} + 3 = 1$

Move all terms not containing $2 \sqrt{x - 1}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$2 \sqrt{x - 1} = 1 - 3$

Subtract $3$ from $1$ .

$2 \sqrt{x - 1} = - 2$

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

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

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

$4 {({(x - 1)}^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

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

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

$4 {(x - 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(x - 1)}^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Rewrite the expression.

$4 {(x - 1)}^{1} = {(- 2)}^{2}$

Simplify.

$4 (x - 1) = {(- 2)}^{2}$

Apply the distributive property.

$4 x + 4 \cdot - 1 = {(- 2)}^{2}$

Multiply $4$ by $- 1$ .

$4 x - 4 = {(- 2)}^{2}$

Simplify the right side.

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

$4 x - 4 = 4$

Solve for $x$ .

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

Add $4$ to both sides of the equation.

$4 x = 4 + 4$

Add $4$ and $4$ .

$4 x = 8$

Divide each term in $4 x = 8$ by $4$ and simplify.

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

Divide $x$ by $1$ .

$x = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$x = 2$

Exclude the solutions that do not make $2 \sqrt{x - 1} + 3 = 1$ true.

$No solution$

Solve for x 2 square root of x-1+3=1

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