Solve by Factoring 4- square root of x=3

$4 - \sqrt{x} = 3$

Step 1

Subtract $3$ from both sides of the equation.

$4 - \sqrt{x} - 3 = 0$

Step 2

Subtract $3$ from $4$ .

$1 - \sqrt{x} = 0$

Step 3

Subtract $1$ from both sides of the equation.

$- \sqrt{x} = - 1$

Step 4

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

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

Step 5

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

Raise $- 1$ to the power of $2$ .

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

Multiply ${(x^{\frac{1}{2}})}^{2}$ by $1$ .

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Raise $- 1$ to the power of $2$ .

$x = 1$