Algebra Examples

$\sqrt{x + 2} + 6 = 5$

Step 1

Move all terms not containing $\sqrt{x + 2}$ to the right side of the equation.

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Step 1.1

Subtract $6$ from both sides of the equation.

$\sqrt{x + 2} = 5 - 6$

Step 1.2

Subtract $6$ from $5$ .

$\sqrt{x + 2} = - 1$

Step 2

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

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

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$x + 2 = 1$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the equation.

$x = 1 - 2$

Step 4.2

Subtract $2$ from $1$ .

$x = - 1$

Step 5

Exclude the solutions that do not make $\sqrt{x + 2} + 6 = 5$ true.

$No solution$