Algebra Examples

\sqrt{x + 3 - x} = 3

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

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}

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

Step 2

Simplify each side of the equation.

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Step 2.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{x + 3 - x}

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

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

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

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

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

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Step 2.2.1.1

Multiply the exponents in

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

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

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Step 2.2.1.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

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

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

Step 2.2.1.1.2

Cancel the common factor of

2

$2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

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

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

Step 2.2.1.1.2.2

Rewrite the expression.

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

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

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

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

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

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

Step 2.2.1.2

Combine the opposite terms in

x + 3 - x

$x + 3 - x$ .

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Step 2.2.1.2.1

Subtract

x

$x$ from

x

$x$ .

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

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

Step 2.2.1.2.2

Add

0

$0$ and

3

$3$ .

3^{1} = 3^{2}

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

3^{1} = 3^{2}

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

Step 2.2.1.3

Evaluate the exponent.

3 = 3^{2}

$3 = 3^{2}$

3 = 3^{2}

$3 = 3^{2}$

3 = 3^{2}

$3 = 3^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise

3

$3$ to the power of

2

$2$ .

3 = 9

$3 = 9$

3 = 9

$3 = 9$

3 = 9

$3 = 9$

Step 3

Since

3 \neq 9

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

No solution

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$