Solve the Rational Equation for x 2 square root of x-3=12

$2 \sqrt{x - 3} = 12$

Step 1

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

${(2 \sqrt{x - 3})}^{2} = 12^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x - 3}$ as ${(x - 3)}^{\frac{1}{2}}$ .

${(2 {(x - 3)}^{\frac{1}{2}})}^{2} = 12^{2}$

Simplify the left side.

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

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

$2^{2} {({(x - 3)}^{\frac{1}{2}})}^{2} = 12^{2}$

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

$4 {({(x - 3)}^{\frac{1}{2}})}^{2} = 12^{2}$

Multiply the exponents in ${({(x - 3)}^{\frac{1}{2}})}^{2}$ .

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

$4 {(x - 3)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(x - 3)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$4 {(x - 3)}^{1} = 12^{2}$

Simplify.

$4 (x - 3) = 12^{2}$

Apply the distributive property.

$4 x + 4 \cdot - 3 = 12^{2}$

Multiply $4$ by $- 3$ .

$4 x - 12 = 12^{2}$

Simplify the right side.

Raise $12$ to the power of $2$ .

$4 x - 12 = 144$

Step 3

Solve for $x$ .

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

Add $12$ to both sides of the equation.

$4 x = 144 + 12$

Add $144$ and $12$ .

$4 x = 156$

Divide each term in $4 x = 156$ by $4$ and simplify.

Divide each term in $4 x = 156$ by $4$ .

$\frac{4 x}{4} = \frac{156}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{156}{4}$

Divide $x$ by $1$ .

$x = \frac{156}{4}$

Simplify the right side.

Divide $156$ by $4$ .

$x = 39$

Solve the Rational Equation for x 2 square root of x-3=12

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