Solve for x -4 square root of x-3=12

$- 4 \sqrt{x - 3} = 12$

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

Simplify ${(- 4 {(x - 3)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 4 {(x - 3)}^{\frac{1}{2}}$ .

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

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

$16 {({(x - 3)}^{\frac{1}{2}})}^{2} = 12^{2}$

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

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

$16 {(x - 3)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$16 {(x - 3)}^{\frac{1}{2} \cdot 2} = 12^{2}$

Rewrite the expression.

$16 {(x - 3)}^{1} = 12^{2}$

Simplify.

$16 (x - 3) = 12^{2}$

Apply the distributive property.

$16 x + 16 \cdot - 3 = 12^{2}$

Multiply $16$ by $- 3$ .

$16 x - 48 = 12^{2}$

Simplify the right side.

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

$16 x - 48 = 144$

Step 3

Solve for $x$ .

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

Add $48$ to both sides of the equation.

$16 x = 144 + 48$

Add $144$ and $48$ .

$16 x = 192$

Divide each term in $16 x = 192$ by $16$ and simplify.

Divide each term in $16 x = 192$ by $16$ .

$\frac{16 x}{16} = \frac{192}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 x}{16} = \frac{192}{16}$

Divide $x$ by $1$ .

$x = \frac{192}{16}$

Simplify the right side.

Divide $192$ by $16$ .

$x = 12$

Step 4

Exclude the solutions that do not make $- 4 \sqrt{x - 3} = 12$ true.

$No solution$

Solve for x -4 square root of x-3=12

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