Algebra Examples

$\sqrt{x + 3} = 7$

Step 1

Subtract $7$ from both sides of the equation.

$\sqrt{x + 3} - 7 = 0$

Step 2

Add $7$ to both sides of the equation.

$\sqrt{x + 3} = 7$

Step 3

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

${\sqrt{x + 3}}^{2} = 7^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

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

${({(x + 3)}^{\frac{1}{2}})}^{2} = 7^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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Step 4.2.1.1.1

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

${(x + 3)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(x + 3)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(x + 3)}^{1} = 7^{2}$

Step 4.2.1.2

Simplify.

$x + 3 = 7^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $7$ to the power of $2$ .

$x + 3 = 49$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$x = 49 - 3$

Step 5.2

Subtract $3$ from $49$ .

$x = 46$