Algebra Examples

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

Step 1

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

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

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x + 3 - x}$ as ${(x + 3 - x)}^{\frac{1}{2}}$ .

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

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(x + 3 - x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(x + 3 - x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.1.2

Combine the opposite terms in $x + 3 - x$ .

Tap for more steps...

Step 2.2.1.2.1

Subtract $x$ from $x$ .

${(0 + 3)}^{1} = 3^{2}$

Step 2.2.1.2.2

Add $0$ and $3$ .

$3^{1} = 3^{2}$

Step 2.2.1.3

Evaluate the exponent.

$3 = 3^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

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

$3 = 9$

Step 3

Since $3 \neq 9$ , there are no solutions.

No solution