Precalculus Examples

$\sqrt{2 x - 5} = 7$

Step 1

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

${\sqrt{2 x - 5}}^{2} = 7^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 5}$ as ${(2 x - 5)}^{\frac{1}{2}}$ .

${({(2 x - 5)}^{\frac{1}{2}})}^{2} = 7^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

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

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Step 2.2.1.1.1

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

${(2 x - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(2 x - 5)}^{\frac{1}{2} \cdot 2} = 7^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 x - 5)}^{1} = 7^{2}$

Step 2.2.1.2

Simplify.

$2 x - 5 = 7^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $7$ to the power of $2$ .

$2 x - 5 = 49$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $5$ to both sides of the equation.

$2 x = 49 + 5$

Step 3.1.2

Add $49$ and $5$ .

$2 x = 54$

Step 3.2

Divide each term in $2 x = 54$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = 54$ by $2$ .

$\frac{2 x}{2} = \frac{54}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{54}{2}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{54}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $54$ by $2$ .

$x = 27$