Algebra Examples

$\frac{\sqrt{4 x + 19}}{2} = 2$

Step 1

Multiply both sides by $2$ .

$\frac{\sqrt{4 x + 19}}{2} \cdot 2 = 2 \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{\sqrt{4 x + 19}}{2} \cdot 2 = 2 \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$\sqrt{4 x + 19} = 2 \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $2$ .

$\sqrt{4 x + 19} = 4$

Step 3

Solve for $x$ .

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Step 3.1

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

${\sqrt{4 x + 19}}^{2} = 4^{2}$

Step 3.2

Simplify each side of the equation.

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Step 3.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x + 19}$ as ${(4 x + 19)}^{\frac{1}{2}}$ .

${({(4 x + 19)}^{\frac{1}{2}})}^{2} = 4^{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Simplify ${({(4 x + 19)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.2.1.1

Multiply the exponents in ${({(4 x + 19)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.2.1.1.1

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

${(4 x + 19)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 3.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.2.1

Cancel the common factor.

${(4 x + 19)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Step 3.2.2.1.1.2.2

Rewrite the expression.

${(4 x + 19)}^{1} = 4^{2}$

Step 3.2.2.1.2

Simplify.

$4 x + 19 = 4^{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

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

$4 x + 19 = 16$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $19$ from both sides of the equation.

$4 x = 16 - 19$

Step 3.3.1.2

Subtract $19$ from $16$ .

$4 x = - 3$

Step 3.3.2

Divide each term in $4 x = - 3$ by $4$ and simplify.

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Step 3.3.2.1

Divide each term in $4 x = - 3$ by $4$ .

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $4$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 3}{4}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 3}{4}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4}$

Decimal Form:

$x = - 0.75$