Basic Math Examples

$2 + 4 z^{\frac{1}{2}} = 0$

Step 1

Subtract $2$ from both sides of the equation.

$4 z^{\frac{1}{2}} = - 2$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(4 z^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${(4 z^{\frac{1}{2}})}^{2}$ .

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Step 3.1.1.1

Apply the product rule to $4 z^{\frac{1}{2}}$ .

$4^{2} {(z^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3.1.1.2

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

$16 {(z^{\frac{1}{2}})}^{2} = {(- 2)}^{2}$

Step 3.1.1.3

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

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Step 3.1.1.3.1

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

$16 z^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Step 3.1.1.3.2

Cancel the common factor of $2$ .

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Step 3.1.1.3.2.1

Cancel the common factor.

$16 z^{\frac{1}{2} \cdot 2} = {(- 2)}^{2}$

Step 3.1.1.3.2.2

Rewrite the expression.

$16 z^{1} = {(- 2)}^{2}$

Step 3.1.1.4

Simplify.

$16 z = {(- 2)}^{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$16 z = 4$

Step 4

Divide each term in $16 z = 4$ by $16$ and simplify.

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Step 4.1

Divide each term in $16 z = 4$ by $16$ .

$\frac{16 z}{16} = \frac{4}{16}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $16$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{16 z}{16} = \frac{4}{16}$

Step 4.2.1.2

Divide $z$ by $1$ .

$z = \frac{4}{16}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $4$ and $16$ .

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Step 4.3.1.1

Factor $4$ out of $4$ .

$z = \frac{4 (1)}{16}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $4$ out of $16$ .

$z = \frac{4 \cdot 1}{4 \cdot 4}$

Step 4.3.1.2.2

Cancel the common factor.

$z = \frac{4 \cdot 1}{4 \cdot 4}$

Step 4.3.1.2.3

Rewrite the expression.

$z = \frac{1}{4}$

Step 5

Exclude the solutions that do not make $2 + 4 z^{\frac{1}{2}} = 0$ true.

$No solution$