Solve for x square root of x-2x+7=0

$\sqrt{x - 2 x + 7} = 0$

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

${\sqrt{x - 2 x + 7}}^{2} = 0^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 2 x + 7}$ as ${(x - 2 x + 7)}^{\frac{1}{2}}$ .

${({(x - 2 x + 7)}^{\frac{1}{2}})}^{2} = 0^{2}$

Simplify the left side.

Simplify ${({(x - 2 x + 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x - 2 x + 7)}^{\frac{1}{2}})}^{2}$ .

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

${(x - 2 x + 7)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 2 x + 7)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Rewrite the expression.

${(x - 2 x + 7)}^{1} = 0^{2}$

Subtract $2 x$ from $x$ .

${(- x + 7)}^{1} = 0^{2}$

Simplify.

$- x + 7 = 0^{2}$

Simplify the right side.

Raising $0$ to any positive power yields $0$ .

$- x + 7 = 0$

Solve for $x$ .

Subtract $7$ from both sides of the equation.

$- x = - 7$

Divide each term in $- x = - 7$ by $- 1$ and simplify.

Divide each term in $- x = - 7$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 7}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$x = 7$