Algebra Examples

$3 \sqrt{2 x + 5} - 15 = 0$

Step 1

Add $15$ to both sides of the equation.

$3 \sqrt{2 x + 5} = 15$

Step 2

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

${(3 \sqrt{2 x + 5})}^{2} = 15^{2}$

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 $\sqrt{2 x + 5}$ as ${(2 x + 5)}^{\frac{1}{2}}$ .

${(3 {(2 x + 5)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(3 {(2 x + 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Apply the product rule to $3 {(2 x + 5)}^{\frac{1}{2}}$ .

$3^{2} {({(2 x + 5)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 3.2.1.2

Raise $3$ to the power of $2$ .

$9 {({(2 x + 5)}^{\frac{1}{2}})}^{2} = 15^{2}$

Step 3.2.1.3

Multiply the exponents in ${({(2 x + 5)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.3.1

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

$9 {(2 x + 5)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Step 3.2.1.3.2

Cancel the common factor of $2$ .

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Step 3.2.1.3.2.1

Cancel the common factor.

$9 {(2 x + 5)}^{\frac{1}{2} \cdot 2} = 15^{2}$

Step 3.2.1.3.2.2

Rewrite the expression.

$9 {(2 x + 5)}^{1} = 15^{2}$

Step 3.2.1.4

Simplify.

$9 (2 x + 5) = 15^{2}$

Step 3.2.1.5

Apply the distributive property.

$9 (2 x) + 9 \cdot 5 = 15^{2}$

Step 3.2.1.6

Multiply.

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Step 3.2.1.6.1

Multiply $2$ by $9$ .

$18 x + 9 \cdot 5 = 15^{2}$

Step 3.2.1.6.2

Multiply $9$ by $5$ .

$18 x + 45 = 15^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $15$ to the power of $2$ .

$18 x + 45 = 225$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $45$ from both sides of the equation.

$18 x = 225 - 45$

Step 4.1.2

Subtract $45$ from $225$ .

$18 x = 180$

Step 4.2

Divide each term in $18 x = 180$ by $18$ and simplify.

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Step 4.2.1

Divide each term in $18 x = 180$ by $18$ .

$\frac{18 x}{18} = \frac{180}{18}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $18$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{18 x}{18} = \frac{180}{18}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{180}{18}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $180$ by $18$ .

$x = 10$