Basic Math Examples

$8 + \sqrt{u + 12} = 4$

Step 1

Move all terms not containing $\sqrt{u + 12}$ to the right side of the equation.

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Step 1.1

Subtract $8$ from both sides of the equation.

$\sqrt{u + 12} = 4 - 8$

Step 1.2

Subtract $8$ from $4$ .

$\sqrt{u + 12} = - 4$

Step 2

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

${\sqrt{u + 12}}^{2} = {(- 4)}^{2}$

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 $\sqrt{u + 12}$ as ${(u + 12)}^{\frac{1}{2}}$ .

${({(u + 12)}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(u + 12)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(u + 12)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(u + 12)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

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.

${(u + 12)}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(u + 12)}^{1} = {(- 4)}^{2}$

Step 3.2.1.2

Simplify.

$u + 12 = {(- 4)}^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 4$ to the power of $2$ .

$u + 12 = 16$

Step 4

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

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Step 4.1

Subtract $12$ from both sides of the equation.

$u = 16 - 12$

Step 4.2

Subtract $12$ from $16$ .

$u = 4$

Step 5

Exclude the solutions that do not make $8 + \sqrt{u + 12} = 4$ true.

$No solution$